Methods and systems for determining energy expenditure during exercise

Abstract

The present disclosure relates to an electronic system and a computer-implemented method for determining a rate of energy expenditure of a person, the method comprising: receiving a first measurement indicative of a rate of transfer of energy from the body of a person to the environment; receiving a second measurement indicative of a measure of the thermal energy stored in the body of the person; calculating a change in the thermal energy stored in the body of the person using the second measurement; and calculating a rate of energy expenditure of the person using the rate of transfer of energy from the body of the person to the environment and the change in the thermal energy stored in the body.

Description

[0001]P28589PC00 26.05.2025 1 METHODS AND SYSTEMS FOR DETERMINING ENERGY EX- PENDITURE DURING EXERCISE FIELD OF THE DISCLOSURE The present disclosure relates to methods and systems for determining the energy ex- penditure of a person during exercise and daily life. BACKGROUND OF THE DISCLOSURE The human body burns energy during exercise and it is of interest to determine the en- ergy or caloric expenditure during exercise. It is important to know the energy expenditure, example for weight loss or weight con- trol, because the total energy expenditure of a person (also referred to as a user) on a given day depends strongly on whether the person exercised or not and the energy ex- penditure during the exercise. By knowing the energy expenditure, a more precise value of a target caloric intake can be calculated, for example to maintain weight or to hit a particular caloric target. It is also important for athletes to know their precise energy expenditure as not refuel- ing sufficiently after exercise can delay or inhibit recovery, potentially lowering perfor- mance in subsequent exercise and limiting training progress. Energy expenditure can be determined reliably and in real-time in a stationary labora- tory setting based on gas exchange, which however requires the person to wear a P28589PC00 26.05.2025 2 mask attached to a gas analyzer. Based on the measured amount of O2 and CO2 ex- haled and inhaled, it is possible to calculate the amount of energy expended by the body. Commonplace methods for calculating the energy expenditure of an exercise activity rely on proxy measurements, for example by using heart rate measurements during ex- ercise and then determining the energy expenditure further using values from tables which may take into account age, sex, height and weight. More sophisticated methods may involve measuring the power output during the exercise, for example by using an ergometer (e.g., attached to a treadmill, rowing machine, bicycle, or footwear. These methods are also imprecise because they rely on a theoretical efficiency in producing the kinetic power which may not apply equally to all individuals. More reliable ways of measuring the energy expenditure have been proposed and rely on more directly monitoring the caloric energy expenditure. The basal metabolic rate produces heat in the body of approximately 100 watts. To maintain a steady body temperature of about 36.5 °C, the body regulates blood flow to the body surface. At rest, blood flow to the skin is restricted and the surface of the skin may be as much as 11 °C cooler than the body core. This results in a lower flux of heat to the environment. With exercise however, the excess heat generated by physical ex- ertion (approximately 80% of the energy needed to contract human muscles is wasted as heat) must be dumped to the environment to maintain a body temperature which is not harmful. Blood flow is diverted to the skin, raising its temperature and the rate at which heat is dumped to the environment is increased. The body typically manages to maintain a nearly constant internal body temperature by balancing the generation of heat by its metabolic process with controlled loss of heat through an combination of P28589PC00 26.05.2025 3 evaporative, convective, radiant, and conductive heat loss mechanisms. At rest in nor- mal room temperature conditions, the body can utilize convective and radiant heat loss (with minor conductive heat loss contributions as well) to regulate body temperature, primarily by control of blood flow to the skin surfaces. If an individual is exercising or is in ambient temperatures above 35°C, the convective and radiant heat loss is inade- quate to control internal temperature and the body begins to utilize evaporative heat loss. Evaporation, both that which occurs insensibly (i.e. without obvious sweating) and sensibly (i.e. with obvious sweating) can provide several fold greater heat loss than the other two mechanisms combined. Therefore, it is important that any method which senses heat flux for determining en- ergy expenditure during exercise can also account for evaporative cooling. WO1994 / 27496A1 proposes a sensor for determining caloric expenditure by measuring heat flux which also takes into account evaporative heat loss, and discloses calculating the energy expenditure using the following formula: Calorie expenditure (k-cal) = total body surface area (m2 ) x fraction of body surface sampled by each sensor (1 for one sensor sensing typical region of heat flux) x heat flux (k-cal / m2 / min.) x time of sensing (min.). More recent art in the field, for example US2014 / 0343861A1 and US6595929B2 dis- close sensors for measuring heat flux with the purpose of determining energy expendi- ture, however they do not disclose any particular methods for ultimately calculating the energy expenditure based on heat flux measurements. While the sensors and systems proposed therein may provide for an acceptable deter- mination of energy expenditure over a long duration such as a whole day, they are not P28589PC00 26.05.2025 4 sufficiently accurate or responsive enough to provide for a useful determination of en- ergy expenditure during exercise, which is of particular importance for persons engag- ing in physical exercise for durations of more than one hour. This is due to the fact that heat flux lags behind energy expenditure because the body acts as a thermal energy buffer. SUMMARY OF THE DISCLOSURE It is an object of the disclosure and embodiments disclosed herein to provide methods and systems for determining the energy expenditure of a person, for example during an exercise activity. In particular, it is an object of the disclosure and embodiments disclosed herein to pro- vide a computer-implemented method and an electronic system for determining the en- ergy expenditure of a person, for example during an exercise activity, which does not have at least some disadvantages of the prior art. The computer-implemented method comprises receiving a first measurement indicative of a rate of transfer of energy from the body of a person to the environment. The method comprises receiving a second measurement indicative of a measure of the thermal energy stored in the body of the person. The method comprises calculating a change in the thermal energy stored in the body of the person using the second meas- urement. The method comprises calculating a rate of energy expenditure of the person using the rate of transfer of energy from the body of the person to the environment and the change in the thermal energy stored in the body. The first measurement (i.e. a first measured value) may originate from a direct or indi- rect measurement of the rate of transfer of energy and be performed by a first sensor P28589PC00 26.05.2025 5 system which may comprise one or more sensors. The first measurement is indicative of and / or related to the rate of transfer of energy from the body of a person to the envi- ronment. The second measurement (i.e., a second measured value) may originate from a direct or indirect measurement of the thermal energy stored in the body of the person and may be performed by the first sensor system and / or a second sensor system. In an embodiment, the second sensor system comprises at least one of the sensors of the first sensor system. The second measurement is indicative and / or related to measure of the thermal energy stored in the body of the person. Calculating the rate of energy expenditure of the person using the rate of transfer of energy from the body of the person to the environment and the change in the thermal energy stored in the body may comprise calculating the rate of energy expenditure as a function of the rate of transfer of energy from the body of the person to the environment and the change in the thermal energy stored in the body. The change in the thermal energy is calculated using the second measurement and a baseline value of a measure of the thermal energy stored in the body and / or a previous second measurement. Calculating the change in the thermal energy may therefore com- prise receiving two (a first and a second) measurements of the measure of the thermal energy in the body, the two measurements having been performed at different time- points, preferably for the same activity of the user, for example a current time-point and a previous time-point (e.g., 10 seconds in the past). In an embodiment, receiving the first measurement indicative of a rate of transfer of en- ergy from the body of the person to the environment comprises receiving a measurement of a flow of thermal energy from the body to the environment. The measurement of a P28589PC00 26.05.2025 6 flow of thermal energy may be a measurement of a heat flux through the skin of the person. The measurement of the heat flux may be performed using a heat flux sensor. The heat flux sensor may be implemented as a monolithic heat flux sensor and / or a differential temperature sensor comprising two temperature sensors spaced apart across a thermal resistance. In an embodiment, receiving the second measurement indicative of a thermal energy stored in the body of the person comprises receiving a measured temperature of the body. Calculating the change in the thermal energy stored in the body may comprise calculating a change in the measured temperature of the body. Determining the change in the temperature may comprise using a difference between a pre-defined baseline temperature and a current temperature measurement and / or using a difference between a previous temperature measurement or the current temperature. The previous temperature measurement may be a previous temperature measurement during a current activity (i.e. within a defined period such as within the past few minutes, preferably within the last minute). The measured temperature of the person may include a core body temperature and / or a skin temperature of a person. The temperature of the person may calculated using the core body temperature and / or the skin temperature, e.g., as a linear combination thereof. The temperature sensor used to determine the temperature of the body may also be used to determine, at least partly, the heat flux through the skin. In an embodiment, the method comprises calculating a total heat flux through the skin of the person, using the heat flux and a pre-defined body surface area factor indicative of P28589PC00 26.05.2025 7 the total surface area of the person. The calculation may be implemented as a function of the heat flux and the pre-defined body surface area factor. The method comprises calculating the rate of energy expenditure of the person as a function of the total heat flux through the skin and the change in the stored thermal energy in the person. In an embodiment, the method comprises calculating the change in the thermal energy stored in the body of the person using a pre-defined heat capacity of the person and the second measurement. In an embodiment, the method comprises calculating the rate of energy expenditure as a function which includes a sum of the heat flux through the skin and the change in the thermal energy stored in the body. Specifically, the method comprises calculating the rate of energy expenditure as a sum of the net outward heat flux through the skin. The rate of change of the stored body heat is a rate of increase of the stored body heat. In an embodiment, the method comprises calculating the rate of change in the thermal energy stored in the body of the person using a heat capacity of the person, wherein the heat capacity of the person is determined using a pre-defined specific heat of a human body and a pre-defined mass or weight of the person. The specific heat of the body may have a known value of approximately 3 kJ / kg / K. The pre-defined mass of the person may be supplied by the person and used in the method. For example, the weight of the person may be retrieved from memory, where it may be stored in conjunction with other user parameters. In an embodiment, the method comprises calculating the rate of change in the thermal energy stored in the body of the person using a heat capacity of the person. The heat capacity of the person is determined using a core heat capacity and a skin heat capacity. The measurement of a temperature of a person includes a core body temperature and a P28589PC00 26.05.2025 8 skin temperature. The core heat capacity is determined using a specific heat of the core of a human, a pre-defined mass of the core of the person, and a change in the core temperature. The skin heat capacity is determined using a specific heat of the skin of a human, a pre-defined mass of the skin of the person, and a change in the skin tempera- ture. The change in the temperatures may be calculated or defined as a difference with respect to a baseline value and / or a previous measurement value. In an embodiment, the method comprises calculating the heat flux through the skin using a pre-defined heat flux correction term, wherein the heat flux correction term depends on a position on the body where the heat flux measurement is performed. The heat flux correction term may be a multiplicative factor between 0.2 and 5. The heat flux correction term may be individually determined using data from a completed exercise activity, in particular during a cool down phase, based on or using a measured heat flux and core body temperature during a cool down phase of a (previous) exercise activity. In an embodiment, the pre-defined heat flux correction term is calculated in particular using the change in the thermal energy stored in the body and the heat flux through the skin during a cool-down phase of a previous exercise activity where the body returns to its resting thermal energy content. The heat flux correction term may specifically calcu- lated using a ratio of the change in the thermal energy to the excess heat flux through the skin. In an embodiment, the method comprises receiving a measurement indicative of a kinetic power output of the person. The method comprises calculating the rate of energy ex- penditure of the person as a function of the total heat flux through the skin, the rate of change of the stored body heat of the person, and the kinetic power output of the person. P28589PC00 26.05.2025 9 The kinetic power output may be measured by an ergometer, e.g., a cycling power meter, a treadmill, or rowing ergometer. The kinetic power output may also be estimated or measured indirectly, for example by motion sensors worn on the body or integrated into equipment such as a running shoe. In an embodiment, the method comprises determining a cumulative energy expenditure using one or more values of the rate of energy expenditure determined during one or more pre-defined periods, respectively. The one or more pre-defined periods may in- clude periods within the duration of an exercise activity. The cumulative energy expendi- ture may in particular be calculated as a sum or integral over one or more rates of energy expenditure. In an embodiment, the method comprises transmitting a message indicative of a meas- ure of energy expenditure, wherein the measure of energy expenditure comprises the rate of energy expenditure and / or the cumulative energy expenditure. The message may be transmitted to a user device and / or a wearable device of the per- son. The method may comprise displaying, on a display, the message. The display may be connected or integrated with a user device or a wearable device of the person. The message may further include an indicator to consume nutrition (e.g., energy gel, energy bar, sports drink). The message may provide an indicator of a number of grams of nutrition to consume, using a defined relationship between the amount of grams of nutrition and calories per gram. For example, the message may be configured to indicate to the person to consume one energy gel of 50 grams (energy gels contain approximately 3 calories per gram for a total of approximately 150 calories per energy gel). P28589PC00 26.05.2025 10 The method may comprise sending the message depending on whether a cumulative energy expenditure has met, reached or satisfied one or more defined energy thresholds, such that the message is sent, for example, only when a defined amount of energy (or multiples thereof) has been expended (e.g. joules or calories burned). For example, a message may be sent for every 200 calories burned. The message may be sent in defined time intervals, for example every 20 minutes. The method may further comprise receiving, from a user device, a reply message indi- cating that fueling has taken place. The reply message may comprise an indicator of how many calories were consumed. The method may comprise determining and / or maintaining a record of a caloric deficit of the person. The method may comprise sending a message if the determined or current caloric deficit is higher than a defined threshold (e.g., 500 calories). The determination of the caloric deficit may take into account a relative exercise intensity as described below in more detail. In an embodiment, the method further comprises calculating a rate of respiratory heat loss. The respiratory heat loss is due to exhalation of warm water vapor. The rate of respiratory heat loss is calculated using the heat flux through the skin, the rate of change of the thermal energy in the body, and a respiratory heat loss factor. The method com- prises calculating the energy expenditure of the person further using the respiratory heat loss. The respiratory heat loss may specifically be calculated as the respiratory heat loss factor multiplied by the sum of the heat flux through the skin and the rate of change of the thermal energy stored in the body. The respiratory heat loss factor depends on personal P28589PC00 26.05.2025 11 and / or environmental factors and is typically in the range of 0.05 – 0.2. A good assump- tion, if no further information is available (e.g., personal and / or environmental factors), is that the respiratory heat loss factor is 0.1. The method may comprise calculating the rate of expenditure as a sum, with the respir- atory heat loss being a term of the sum. In an embodiment, the method comprises receiving a plurality of measurements of the heat flux through the skin and / or a plurality of measurements of the temperature. At least some of the measurements were performed at different positions on the body of the person. The method comprises combining the plurality of measurements of the heat flux (e.g., calculating a single value for the heat flux using the plurality of measurements, for example as a linear combination) and calculating a single value for the temperature using the plurality of temperature measurements. A particular heat flux and temperature meas- urement may be performed at the same location, preferably by a single sensor device. Several such sensor devices may be worn on the body of the person. Each individual measurement may be subject to non-linear scaling prior to (linear) combination. The plu- rality of measurements may be processed and / or combined to generate a single output value using an algorithm trained using machine learning. The present disclosure also relates to an electronic system for determining a rate of energy expenditure of a person. The electronic system comprises a processor config- ured to perform one of the methods described herein. In an embodiment, the electronic system further comprises a wearable device including a sensor system configured to determine the heat flux through the skin and a tempera- ture of the person. The sensor system is worn on the body of the person. P28589PC00 26.05.2025 12 The sensor system may be configured to directly measure the skin temperature and may be configured to calculate, using the skin temperature and the heat flux, the core body temperature, for example as described in the publication Etienne, S., Oliveras, R., Schiboni, G. et al. Free-living core body temperature monitoring using a wrist-worn sen- sor after COVID-19 booster vaccination: a pilot study. BioMed Eng OnLine 22, 25 (2023). https: / / doi.org / 10.1186 / s12938-023-01081-3. The electronic system may be configured to receive further physiological signals, includ- ing HR, HRV, galvanic skin response, accelerometer, IR, ECG, blood pressure, and / or ambient measurements. In an embodiment, the electronic system comprises a plurality of wearable devices. Each wearable device includes a sensor system, and the processor is configured to receive data from the plurality of sensor systems of the wearable devices. The sensor systems are arranged at different positions on the body of the same user. In an embodiment, the sensor system comprises a heat flux sensor configured to deter- mine heat flux. The heat flux sensor may be implemented using a chip comprising a series of p- and n- doped semiconductors where the sensor functions on the basis of the Seebeck effect. The heat flux sensor may alternatively be implemented using two stacked temperature sensors separated by a thermal resistance. The sensor system may be configured to determine the core body temperature using the heat flux and a skin temperature and a known algorithm. The two stacked temperature sensors may also be used to determine the skin tempera- ture. In particular, the temperature sensor closest to the skin may be used to determine the skin temperature. P28589PC00 26.05.2025 13 In an embodiment, the electronic system further comprises one or more of a PPG or another optical sensor, an ECG sensor, a blood lactate sensor, a galvanic skin response sensor, a sweat rate sensor, one or more further skin temperature sensors, an ambient temperature sensor, or an accelerometer. The additional sensors are preferably inte- grated into the wearable device. In an embodiment, the wearable device comprises a strap for securing the wearable device to the body of a human, in particular a chest strap, an arm strap, or a wrist strap. Alternatively or additionally, an adhesive film and / or adhesive tape may be used to attach the wearable device to the body. In an embodiment, the processor is integrated into the wearable device. In an embodiment, the wearable device includes a wireless communications module configured to generate and transmit a message indicative of a measure of energy ex- penditure, wherein the measure of energy expenditure comprises one or more of the following: the rate of energy expenditure or the cumulative energy expenditure. In an embodiment, the message may be displayed on a display, in particular a display of a user device such as a personal electronic device. The personal electronic device may be implemented as smart watch, exercise computer, mobile phone, or laptop via web interface, for example. The electronic system may comprise such a user device configured to receive the mes- sage and display the message. P28589PC00 26.05.2025 14 In an embodiment, the electronic system further comprises a separate electronic device, the processor integrated into the separate electronic device. The wearable device in- cludes a wireless communications module configured to transmit a message including the heat flux and the temperature to the separate electronic device. In addition to computer-implemented methods and an electronic system for implement- ing the computer-implemented methods, the present disclosure also relates to a com- puter program product for performing one or more of the methods described herein. The computer program product comprises computer program code configured to control a processor such that the processor performs one or more of the methods described herein. The present disclosure also relates to a non-transitory computer readable medium hav- ing stored thereon computer program code configured to control a processor such that the processor performs one or more of the methods described herein. The embodiments described above apply to one or more of the methods herein. In par- ticular, the features of a specific embodiment are not limited to the particular method with which they may be construed to relate to, rather, the skilled person knows that the teach- ing of the specific embodiment may also be applied in another method. BRIEF DESCRIPTION OF THE DRAWINGS The herein described disclosure will be more fully understood from the detailed descrip- tion given herein below and the accompanying drawings, which should not be considered limiting to the invention described in the appended claims. The drawings in which: Fig.1 shows a diagram illustrating a human and indicating several positions on the human body where a wearable device as described herein may be worn; P28589PC00 26.05.2025 15 Fig.2 shows schematically a front view of a wearable device comprising a sensor system; Fig.3 shows schematically a side view of a wearable device comprising a sensor system and indicating a heat flux through the sensor system; Fig.4 shows a block diagram illustrating schematically an electronic system com- prising a wearable device and a processor; Fig.5 shows a block diagram illustrating schematically an electronic system com- prising a wearable device having an integrated processor; Fig.6 shows a diagram illustrating schematically an electronic system including a wearable device connected to a user device, the user device including a pro- cessor; Fig.7 shows a diagram illustrating schematically an electronic system including a wearable device, a server computer, and a user device; Fig.8 shows a diagram illustrating schematically an electronic system including a wearable device with a display and a server computer; Fig.9 shows a block diagram illustrating schematically a sensor system comprising a heat flux sensor and a skin temperature sensor; Fig.10 shows a block diagram illustrating schematically a sensor system comprising a heat flux sensor, a skin temperature sensor, and optional further sensors; Fig.11 shows a flow diagram illustrating a method for determining a rate of the en- ergy expenditure during exercise; Fig.12 shows a flow diagram illustrating a method for determining a cumulative en- ergy expenditure during exercise; P28589PC00 26.05.2025 16 Fig.13 shows a flow diagram illustrating a method for determining a rate of the en- ergy expenditure during exercise further taking into account the kinetic power output; Fig.14 shows a flow diagram illustrating a method for determining a rate of the en- ergy expenditure during exercise further taking into account the respiratory heat loss; Fig.15 shows a flow diagram illustrating a method for determining a correction term for a skin temperature measurement; Fig.16 shows a flow diagram illustrating a method for setting up a user device; Fig.17 shows a flow diagram illustrating a method for using the user device during an activity; Fig.18 shows a chart illustrating the heat flux during an activity as determined using a method described herein; Fig.19 shows a flow diagram illustrating a method for calculating a heat flux correc- tion term; Fig.20 shows six time-series charts showing various measurement data and values derived therefrom during an exercise activity; and Fig.21 shows three time-series charts showing energy expenditure data used for calculating the heat flux correction term. DESCRIPTION OF THE EMBODIMENTS Reference will now be made in detail to certain embodiments, examples of which are illustrated in the accompanying drawings, in which some, but not all features are shown. Indeed, embodiments disclosed herein may be embodied in many different forms and P28589PC00 26.05.2025 17 should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal require- ments. Whenever possible, like reference numbers will be used to refer to like compo- nents or parts. Fig.1 shows a human body 8. Illustrated are a number of possible positions 81, 82, 83, 84, 85 on the body 8 where a wearable device 2A, 2B, 2C, 2D, 2E can be worn, however other positions are possible. Typically, a single wearable device 2A, 2B, 2C, 2D, 2E is worn at one of the positions 81, 82, 83, 84, 85. The positions 81, 82, 83, 84, 85 include a chest area 81, in particular on the left chest area (the so-called apical region), a wrist region 82 (in particular on a dorsal side of the wrist), an upper arm 83, an upper leg 84, and a lower leg 85. Other possible positions include the head (e.g., the forehead or a temple region), forearm, ankle, finger, fingertip, earlobe, or inside the ear. The wearable device 2A, 2B, 2C, 2D, 2E is preferably worn in direct body contact (in particular, direct skin contact) for best results. However, the wearable device 2A, 2B, 2C, 2D, 2E may also be worn over one or more layers of clothing. Depending on the embodiment, the wearable device 2A, 2B, 2C, 2D, 2E is implemented as a single device, or implemented as a distributed device with one or more connected parts. In an embodiment where the wearable device 2A, 2B, 2C, 2D, 2E is worn on a limb of the body 8 or worn on the torso, the wearable device 2A, 2B, 2C, 2D, 2E is typically affixed to the body 8 by means of a strap or band. The wearable device 2A, 2B, 2C, 2D, 2E may also be at least partially integrated into a garment, in particular a garment de- signed for being worn in skin contact. P28589PC00 26.05.2025 18 In an embodiment where the wearable device 2A, 2B, 2C, 2D, 2E is configured to be worn on the wrist, the wearable device 2A, 2B, 2C, 2D, 2E may be implemented in the form of an electronic bracelet, electronic cuff, or electronic watch, for example. In partic- ular, the wearable device 2A, 2B, 2C, 2D, 2E can be implemented as a health tracker, fitness tracker, and / or a smart watch (as is depicted in Fig.8, for example). In an embodiment where the wearable device 2A, 2B, 2C, 2D, 2E is configured to be worn on the head, in particular on a forehead or a temple region, the wearable device 2A, 2B, 2C, 2D, 2E may be implemented as an electronic headband, electronic glasses (i.e., smart glasses), an electronic hat, or an electronic helmet, for example. As is explained below, the wearable device 2A, 2B, 2C, 2D, 2E includes a sensor system (not shown). The sensor system may include one or more sensors directly integrated into the wearable device 2A, 2B, 2C, 2D, 2E (i.e. having a housing in common with the 2A, 2B, 2C, 2D, 2E). However, the wearable device 2A, 2B, 2C, 2D, 2E may also include one or more auxiliary sensors which are not directly integrated into the wearable device 2A, 2B, 2C, 2D, 2E but are connected to the wearable device 2A, 2B, 2C, 2D, 2E using a wired or wireless data communication system. As shown in Figs.2 and 3, the wearable device 2 has a substantially rectangular housing having a front side F and a back side B. The wearable device 2 is thin in comparison to its lateral dimensions. The wearable device 2 comprises a sensor system 3, in particular including a heat flux sensor 31 and a skin temperature sensor 32. The heat flux sensor 31 is configured to measure the heat flux from the skin to the environment. The skin temperature sensor is configured to measure the skin temperature. The wearable device and / or sensor system 3 may further a core body temperature sensor, which measures the core body temperature. The various sensors perform measurements, the results or outputs of which may be recorded, transmitted or otherwise provided as one or more P28589PC00 26.05.2025 19 values indicative of the heat flux, skin temperature or core body temperature, respec- tively. The core body temperature sensor may be implemented using a heat flux sensor 31 and a skin temperature sensor 32 as is explained in more detail with reference to Fig.9. The sensor system 3 can comprise further sensors as is explained in more detail with refer- ence to Fig.10. When worn on a body 8, the back side B faces the body, preferably in direct skin contact with the body 8. The arrow indicates the heat flux HF which flows from the body 8 through the wearable device 2 from the back side B to the front side F. Figs.4 - 8 show examples of an electronic system 1. The electronic system 1 comprises at least one processor 11 configured to carry out one or more steps and / or functions as described herein. Depending on its configuration, the electronic system 1 further includes various compo- nents, such as a memory 12, a communication interface, and / or a user interface. The components of the electronic system 1 are connected to each other via a data commu- nication system, such that they can transmit and / or receive data. The term data communication system relates to a communication system that facilitates data communication between two components, devices, systems, or other entities. De- pending on its configuration, the data communication system is wired and includes a wired connection, such as a cable and / or a system bus, and / or includes a wireless con- nection, such as Bluetooth (BT), Bluetooth Low Energy (BLE), ANT+, WiFi, RFID, etc. The data communication system may further include communication modules for com- munication via networks, such as local area networks (LANs), mobile radio networks P28589PC00 26.05.2025 20 (e.g., GSM, GPRS, CDMA2000, EDGE, and / or UTMS), and / or the Internet 5. The Inter- net 5 includes, depending on the implementation, intermediary networks. The processor 11 may comprise a system on a chip (SoC), a central processing unit (CPU), and / or other more specific processing units such as a graphical processing unit (GPU), application specific integrated circuits (ASICs), or reprogrammable processing units such as field programmable gate arrays (FPGAs). The memory 12 comprises one or more volatile (transient) and / or non-volatile (non-tran- sient) storage components. The storage components may be removable and / or non- removable, and can also be integrated, in whole or in part with the processor 11. Exam- ples of storage components include RAM (Random Access Memory), flash memory, hard disks, data memory, and / or other data stores. The memory 12 comprises a non- transitory computer-readable medium having stored thereon computer program code configured to control the processor 11, such that the electronic system 1 performs one or more steps and / or functions as described herein. Depending on the embodiment, the computer program code is compiled or non-compiled program logic and / or machine code. As such, the electronic system 1 is configured to perform one or more steps and / or functions. The computer program code defines and / or is part of a discrete software application. One skilled in the art will understand that the computer program code can also be dis- tributed across a plurality of software applications (Apps). In an embodiment, the com- puter program code further provides interfaces, such as APIs, such that functionality and / or data of the electronic system 1 can be accessed remotely, such as via a client application or via a web browser. P28589PC00 26.05.2025 21 While particular steps and / or functions are described herein as being performed by a particular component or device of the electronic system 1, particular steps and / or func- tions may be performed in other components or devices of the electronic system 1 in whole or in part. Further, particular steps disclosed as being performed by the processor 11 may be performed by the wearable device 2. Additionally or alternatively, particular steps as disclosed as being performed by the processor 11 may be performed by a plu- rality of processors 11, in particular a plurality of processors 11 distributed across one or more devices of the electronic system 3. As depicted in Figs.4 - 8, the electronic system 1 comprises the wearable device 2. The wearable device includes the sensor system 3. The wearable device 2 may include a communications module configured for data com- munication with other devices, in particular with other devices of the electronic system 1, using the data communication system. Depending on the embodiment, the communica- tions module may be configured for wired and / or wireless communication. Depending on the embodiment, the wearable device 2 may also include further electronic components, in particular a power source such as a battery. Other electronic compo- nents include, for example, a user interface configured to receive user input and / or pro- vide information to the user, for example comprising user input means such as a touch screen, buttons, a rotary wheel, etc. The user interface may provide information to the user by means of a display (e.g., a screen, a touch screen, and / or an AR display system), a loudspeaker, or haptic feedback (e.g. using vibrations). In an embodiment, the wearable device 2 further comprises modules configured to de- termine a current time, an orientation of the wearable device 2, a location of the wearable device 2 (e.g. using a GNSS receiver, signal strengths of nearby WLAN access points, P28589PC00 26.05.2025 22 or signal strengths of nearby mobile radio transceivers), and / or ambient conditions, which ambient conditions comprise an air temperature, pressure and / or humidity. Additionally, depending on the embodiment, the wearable device 2 comprises a pro- cessing unit separate from the processor 11. The processing unit is, for example, imple- mented as a microprocessor running program code (for example, embedded program code). As such, the processing unit may be configured to perform one or more steps and / or functions as described herein. The processing unit is connected to the sensor system 3 and other electronic components of the wearable device 2, including the bat- tery, user interface, communication module, etc. Additionally, depending on the embodiment, the wearable device 2 comprises a memory connected to the processing unit configured to record a sensor output, comprising an output of the one or more sensors of the sensor system 3. Depending on the embodi- ment, the memory is integrated into the processing unit and / or the sensor system 3. In particular, the memory is configured to record the heat flux, core body temperature and the skin temperature measurement. These may be recorded in the form of one or more values, respectively. The memory may be further configured to record one or more ad- ditional measurements as measured by the sensor system 3, in particular from those optional additional sensors of the sensor system described with reference to Fig. 10 below. Depending on the embodiment, the sensor output from one or more sensors of the sen- sor system 3 is pre-processed (e.g., adjusted, corrected, filtered, statistically analyzed, summarized, compressed, and / or combined with an output of one or more other sensor outputs) in the wearable device 2. P28589PC00 26.05.2025 23 Depending on the embodiment, the sensor output from a sensor of the sensor system 3 may be used to directly determine one or more physiological signals of the person. For example, a skin temperature sensor may directly measure the skin temperature, or an ECG sensor may be used to determine both the heart rate and the heart rate variability. The sensor output from the sensor of the sensor system 3 may also be combined with one or more other sensor outputs from other sensors of the sensor system 3 to determine a physiological signal of the person. For example, the sensor output from a plurality of skin temperature sensors may be combined to determine an average skin temperature. In another example, the core body temperature measurement may be determined using a sensor output from one or more sensors (i.e. as a function of a sensor output from one or more sensors), in particular sensor output from a heat flux sensor 31 and a sensor output from a skin temperature sensor 32. The core body temperature measurement value may also be adjusted using a calibration file. The skin temperature sensor may directly provide the sensor output from the skin tem- perature sensor 32. However, the skin temperature measurement (represented as one or more values) may also be corrected based on the position where the skin temperature sensor 32 is worn. The skin temperature measurement value may also be adjusted using a calibration file. The sensor output from the sensor system 3 may be pre-processed, for example using LOWESS (Locally Weighted Scatterplot Smoothing), sometimes called LOESS (locally weighted smoothing) to remove outliers. In another example, a plurality of sensor measurements, sensor output values and / or physiological signal values are recorded over a pre-defined time interval and averaged to generate a single sensor output value and / or physiological signal value, which is then P28589PC00 26.05.2025 24 recorded in the memory. Alternatively, or additionally, a representative sensor output value and / or physiological signal value is selected as the sensor output value and / or physiological signal value, respectively. Preferably, sensor output values and / or physio- logical signal values are averaged across a period of ten seconds and recorded as a single sensor output value and / or a single physiological signal value, respectively. The skilled person is aware that other periods of time in the same general orders of magni- tude (i.e. from approximately 1 second to approximately 100 seconds) are, depending on the embodiment, more appropriate than the example value of ten seconds given above. By not recording every single sensor output value and / or physiological signal value, the amount of data stored in the memory of the wearable device 2 is reduced. Further, the amount of data transmitted to the processor 11 is also reduced. Some sen- sor output values may be averaged across different time periods, for example while heart rate may be measured (or averaged) every 10 seconds while core body temperature and skin body temperature are measured (or averaged) every 30 seconds. In an embodiment, the sensor system 3 is configured to record the output of a particular sensor only and / or record a particular physiological signal only when a particular set of circumstances apply. These circumstances include, for example, when the individual is active (which may be determined by an accelerometer and / or a heart rate), when the core body temperature and / or skin temperature is elevated (i.e. when the core body tem- perature exceeds a pre-defined threshold and / or the skin temperature exceeds a pre- defined threshold), when the heat flux rises above a baseline, when the thermal energy stored in the body begins to rise above a baseline, when the rate of transfer of energy from the body to the environment rises above a baseline value, and / or when a signal is received in the wearable device 2 to begin recording. In particular, the recording of the heat flux, the core body temperature and / or the skin temperature may depend on the heart rate being elevated, in particular higher than a pre-defined heart rate threshold, thereby indicating that the person is active. P28589PC00 26.05.2025 25 Depending on the embodiment, the functions and / or steps described above related to adjustment, correction, pre-processing, filtering, statistically analyzing, and / or combining sensor outputs are executed in the wearable device 2 itself (in particular in the pro- cessing unit of the wearable device 2) or in the processor 11 of the electronic system 1. Depending on the embodiment, the sensor system 3 of the wearable device 2 further comprises sensors configured to measure a heart rate, a heart rate variability, a skin perfusion, a breathing rate, respiratory rate, a blood pressure, and / or aspects of electro dermal activity. As shown in Fig.4, the electronic system 1 comprises the wearable device 2, the pro- cessor 11, and the memory 12. The electronic system 1 may be implemented in a single device, or may be implemented in a plurality of devices communicatively coupled to each other, for example using the data communication system as described herein. For ex- ample, the electronic system 1 is implemented as a wearable device 2 connected to a user device 4 (as described in Fig.6 in more detail). As shown in Fig.5, the electronic system 1 comprises a wearable device 2, the wearable device 2 including the sensor system 3, the processor 11, and the memory 12. The wear- able device 2 may be implemented in a single device, or may be implemented in a plu- rality of devices communicatively coupled to each other, for example using the data com- munication system as described herein. For example, the electronic system 1 is imple- mented as a wrist worn device, for example an electronic bracelet or an electronic watch. Popular examples of such wrist worn devices include fitness trackers and smart watches. As shown in Fig.6, the electronic system 1 may be distributed between a wearable de- vice 2 and a user device 4. One or more of the functions and / or steps described herein may be performed, in whole or in part, on the wearable device 2 and other functions P28589PC00 26.05.2025 26 and / or steps described herein may be performed, in whole or in part, in the user device 4. In particular, the steps and / or functions described herein as being performed on the processor 11 may be performed either in the wearable device 2 (the processor 11 being implemented in the wearable device 2) or in the user device 4 (the processor 11 being implemented in the user device 4). Additionally, in the case that the processor 11 is im- plemented in the user device 4, the wearable device 2 may have a separate processing unit as described herein, with the functions and / or steps described herein being per- formed either in the processing unit of the wearable device 2, the processor of the user device 4, or in conjunction between the two devices 2, 4. Depending on the embodiment, the user device 4 is implemented as a mobile device, for example a mobile radio phone (e.g., a smart phone running an iOS or Android operating system), a tablet computer, a laptop computer, a smart watch, a fitness watch, a sports computer (e.g., an electronic sports watch, a cycling computer, or a rowing computer). The user device 4 may include a display 41, for example implemented as a touch screen. The user device 4 is configured to be connected to the wearable device 2 either using a wired or wireless data communication system. As shown in Fig.6, the electronic system 1 includes a wearable device 2, a user device 4, and a server computer 6. The wearable device 2 is connected to the user device 4 using the data communication system, in particular a using a short range wireless com- munications protocol such as Bluetooth LE (low energy) or ANT+. The user device 4 is connected to the server computer 6 using a data communication system, in particular via an intermediary network 5 which may include a mobile radio network and / or the Internet. The server computer 6 may be located remotely from the wearable device 2 and the user device 4, for example in a data processing facility such as a cloud computing center. P28589PC00 26.05.2025 27 As depicted in Fig.7, the processor 11 and the memory 12 may be implemented in the server computer 6. However, at least some of the steps and / or functions performed by the processor 11 may be performed, in whole or in part, in the user device 4 and / or in conjunction with the user device 4. For example, the user device 4 may perform pre- processing of the sensor data or physiological signals. The user device 4 may merely forward data received from the wearable device 2 to the server computer 4 (forwarding the data may include buffering, e.g., temporarily storing, the data). For example, the server computer 6 may perform data processing and transmit messages to the user de- vice 4 based on the processed data. This is depicted in by the dashed box which indi- cates a distributed processing environment 7. As depicted in Fig.8, the electronic system 1 may comprise a wearable device 2 imple- mented as a smart device, in particular a smart watch comprising a user interface 23 (for example including a touch screen). The wearable device 2 is connected to the server computer 1 via an intermediary network 5 which may include a mobile radio network the Internet. To that end, the wearable device 2 includes a mobile radio transceiver, for ex- ample configured to communicate using one or more digital cellular technologies (e.g., GSM, GPRS, CDMA2000, EDGE, and / or UTMS). The steps and / or functions described herein may be performed by the wearable device 2, the server computer 6, and / or a combination of both. Figs.9 and 10 show block diagrams illustrating schematically a sensor system 3 of the wearable device 2. As described, the sensor system 3 may be wholly integrated into the wearable device 2 (integrated in the sense of structural integration, e.g., that they share a common housing with the wearable device 2) or may be partially integrated, such that at least some sensors are integrated into the wearable device 2 while some other sen- sors are separately arranged and connected to the wearable device 2 using a data com- munication system as described herein. P28589PC00 26.05.2025 28 The sensor system 3 is configured to measure physiological signals of the person. A sensor output of a particular sensor of the sensor system 3 may directly provide a meas- urement of one or more physiological signals, such as a skin temperature sensor directly providing the physiological signal of the skin temperature of the human. In another ex- ample, a sensor output of a particular sensor may directly provide a measurement of multiple physiological signals, for example an electrocardiogram (ECG) may provide a heart rate and a heart rate variability, or a photo plethysmograph (PPG) may provide a heart rate, a heart rate variability, a skin perfusion, and / or a breathing rate. In yet another example, a sensor output of a particular sensor may be combined with another sensor output of another sensor to determine a physiological signal, such as the core body temperature being determined using a sensor output of a heat flux sensor and a sensor output of a skin temperature sensor. A mean body temperature may be deter- mined using a combination of the core body temperature and the skin temperature, for example a linear combination. As depicted in Fig.9, the sensor system 3 includes a heat flux sensor 31 and a skin temperature sensor 32. The heat flux sensor 31 is preferably implemented using a Seebeck element, in particular comprising a series of p- and n- doped semiconductors. The heat flux sensor 31 and the skin temperature sensor 32 are preferably implemented using the sensor unit disclosed in WO2018114653A1, which publication is included herein by reference in its entirety. The heat flux sensor 31 may alternatively be implemented using a plurality of tempera- ture sensors. For example, the plurality of temperature sensors includes a first tempera- ture sensor arranged such that it is in contact with the body, in particular in contact with P28589PC00 26.05.2025 29 the skin, when the wearable device 2 is worn, and a second temperature sensor ar- ranged with a thermally conductive layer of a pre-determined thermal conductivity be- tween the first and second temperature sensor, the second temperature sensor prefera- bly being exposed to the environment (i.e. by being arranged on or in thermal contact with a surface of the wearable device 2 opposite the first temperature sensor). The sensor system 3 may further include a photo plethysmograph (PPG) sensor. The PPG sensor may be integrated in the same device as the other sensors, for example in the wearable device 2, or be arranged separately from the other sensors. In particular, the PPG sensor may be implemented in a wrist worn device, such as a fitness tracker or smart watch. The PPG sensor may alternatively be arranged in an electronic ring worn on a finger. The PPG sensor is configured to communicate, using the data communica- tion system as described herein, depending on the embodiment, with the wearable de- vice 2, with the user device 4, and / or with the processor 11. The sensor system 3 may further include an ECG sensor. The ECG sensor may be in- tegrated in the same device as the other sensors of the sensor system 3, for example in the wearable device 2, or be arranged separately from the other sensors. In particular, the ECG sensor may be implemented in a second wearable device worn in contact with the torso, in particular the chest, of the human. The second wearable device may be attached to the human by way of a strap or belt. The (first) wearable device 2 may be attached to the human on the same strap of belt. The ECG sensor is configured to com- municate, using the data communication system as described herein, depending on the embodiment, with the wearable device 2, with the user device 4, and / or with the proces- sor 11. P28589PC00 26.05.2025 30 Depending on the embodiment, the sensor system 3 may be configured to determine additional physiological signals using one or more sensors, including a galvanic skin re- sponse, a sweat rate, a breathing rate, an oxygen saturation, a blood oxygen saturation, a blood pressure, a glucose concentration, or a lactate concentration. The sensor system 3 may further be configured to measure other values, including en- vironmental conditions, such as an ambient air temperature using an ambient tempera- ture sensor 33, and an ambient humidity, or values related to a location or movement of the human. The location may be determined using a GNSS receiver (e.g. a GPS re- ceiver). The movement may be determined by means of an inertial measurement unit (IMU) comprising, for example, a three axis accelerometer, a gyroscope, and / or a mag- netic field sensor. Figs.11 to 17 and 19 show flow diagrams illustrating methods 110, 120, 130, 140, 150, 160, 170, 190 each comprising a number of steps performed by the electronic system 1, in particular the wearable device 2 and / or the processor 11. The methods 110, 120, 130, 140, 150, 160, 170, 190 may be performed at a given time- point. The time-point may be during a period of elevated bodily activity, for example dur- ing an exercise activity. The methods 110, 120, 130, 140, 150, 160, 170, 190 may also be performed for, or during, a defined period, such as a number of hours or an entire day. The methods 110, 120, 130, 140, 150, 160, 170, 190 or particular steps of the meth- ods may be performed once, in an intermittent fashion, or in a continuous fashion. The methods 110, 120, 130, 140, 150, 160, 170, 190 or particular steps thereof may take place on demand, i.e. when an appropriate signal is received from a user via user input (e.g. via a user device, such as a smart phone or exercise computer), from events and / or triggers occurring in the electronic system due to other processes or functions (e.g., P28589PC00 26.05.2025 31 based on a time of day, based on detected movement or the beginning of an exercise activity), and / or by an external device which triggers the method or steps. The methods 110, 120, 130, 140, 150, 160, 170, 190 or particular steps thereof may be performed automatically, for example at pre-determined times or after pre-determined periods. The methods 110, 120, 130, 140, 150, 160, 170, 190 may be performed using “live” data, i.e. data which has just been measured and / or received from the wearable device. Thereby, the person may be informed of their current physiological state, in particular with regards to energy expenditure. The methods 110, 120, 130, 140, 150, 160, 170, 190 may additionally or alternatively be performed retrospectively, i.e. using past recorded data, such that the person may analyze time periods in the past, for example a defined day or week in the past, or a past activity, in order to determine their energy expenditure during that time period. Fig.11 shows a flow diagram illustrating a method 110 which includes a number of steps S11-S15 for calculating a rate of energy expenditure. In steps S11A and S11B the wearable device 2, in particular the sensor system 3 of the wearable device 2, measures a heat flux, in particular a heat flux HF, and a temperature of a person, respectively. The temperature may comprise a core body temperature CBT and / or a skin temperature ST of the person. The core body temperature CBT may be determined using the heat flux HF and a skin temperature ST. Preferably, the heat flux HF is measured using a heat flux sensor in skin contact with the person. Preferably, the heat flux sensor is arranged at the same location on the body as the skin temperature sensor, e.g., inside the same wearable device 2. Specifically, the core body temperature CBT may be determined as a function of the heat flux HF and the skin temperature ST, in particular using known algorithms or models, for P28589PC00 26.05.2025 32 example using a resistive model of heat flux from a core of the body to the environment via the skin. For example, using the following function: ^^^ = ^^ + ^^ × ^^ (1)where RB is the thermal resistance of the human body at the defined location on the human body. In another example, the core body temperature CBT is determined from the skin temper- ature ST and the heat flux HF using a statistical algorithm based on the skin temperature ST and the heat flux HF, wherein the statistical algorithm has been generated using machine learning. The core body temperature CBT may additionally be determined or calculated using the heart rate HR. The core body temperature CBT may also be determined using a temperature sensor in the form of a swallowable device with a wireless transponder which wirelessly transmits the core body temperature to the wearable device 2. The temperature of the person used in the subsequent steps of the method may include the core body temperature CBT and / or the skin temperature ST. Additionally or alterna- tively, the temperature of the person may include a value calculated using the core body temperature CBT and / or the skin temperature ST, for example a linear combination of the core body temperature CBT and / or the skin temperature ST. In step S12, the heat flux HF and the temperature(s) are transmitted, in a transmission T1, from the wearable device 2 to the processor 11. The transmission T1 is a wired or wireless transmission, in particular using the data communication system as described herein. In an embodiment where the processor 11 and the wearable device 2 are inte- grated, i.e. part of the same device, steps S12 and S13 may be omitted. P28589PC00 26.05.2025 33 The wearable device 2 may be configured to perform steps S11 and S12 continuously, for example at 1 second intervals. As described herein, the wearable device 2 may be configured to pre-process the measured heat flux HF and temperature(s). Depending on the embodiment, the wearable device 2 may be configured to transmit other sensor outputs or other physiological signals as described herein to the processor 11. In particular, the transmission T1 from the wearable device 2 to the processor 11 is a transmission from a communication module of the wearable device 2 to a communica- tion module connected to the processor 11. For example, the communication module connected to the processor 1 may be a communication module of the user device 4 or the server computer 6. The transmission T1 may be direct or indirect, for example a direct transmission to the server computer 6 using a mobile radio network, or an indirect transmission via the user device 4. In an embodiment, multiple wearable devices 2 may be worn by the person, for example in positions 81, 82, 83 as shown in Fig.1 In step S13, the processor 11 receives the heat flux and the temperature(s) from the wearable device 2, in particular using the data communication system. In an embodiment, the processor 11 receives multiple heat flux and temperature meas- urements from multiple wearable devices 2, respectively. The processor 11 is configured to combine the multiple heat flux measurements and combine the multiple temperature measurements, respectively, to determine a single heat flux value used for further cal- culation and to determine a single temperature value (respectively a single core temper- ature value and a single skin temperature value) used for further calculation. P28589PC00 26.05.2025 34 Each of the multiple heat flux measurements may be subject to individual scaling using a heat flux correction term which depends on the body position where the wearable de- vice is worn. Specifically, each wearable device 2 is identified as being worn at a partic- ular position on the body, and the processor 11 applies the appropriate correction factor. For example, the heat flux correction term may be a multiplicative factor of between 0.3 and 10. The heat flux correction term may be constant, i.e. invariant to each of the meas- ured heat fluxes. The heat flux correction term may be linearly or piece-wise linearly dependent on the measured heat flux(es). In particular, the heat flux correction term may be a multiplicative scaling factor which is smaller than 1 for a measured heat flux below a defined heat flux threshold, and above 1 for a measured heat flux above the defined heat flux threshold. The defined heat flux threshold may be, for example, approximately in the range of 100 to 300 W / m2. For example, if the measured heat flux(es) is below 100 W / m2, the heat flux correction term may be a multiplicative factor of between 0.3 and 0.7, preferably 0.5. Thereby, a measured heat flux of 100 W / m2 may be corrected such that, after scaling using the heat flux correction term, the resulting corrected heat flux is 50 W / m2. If the measured heat flux(es) is above 500 W / m2, the heat flux correction term may be a multiplicative scaling factor of between 3 and 6, for example 4.5, such that the resulting corrected heat flux is 2250 W / m2. The multiplicative scaling factor may be linearly dependent on the measured heat flux between the defined factors of 0.5 at 100 W / m2 and 4.5 at 500 W / m2, such that, for example, at 300 W / m2 the heat flux correction term is 2.5. After individual scaling, the heat flux measurements may be combined as a linear com- bination, e.g. a single heat flux value is calculated on the basis of a linear combination of the plurality of (scaled) heat flux measurements. P28589PC00 26.05.2025 35 The single heat flux value may then be subject to further non-linear scaling, prior to being used for further calculation as described herein. The further non-linear scaling may be implemented by an algorithm trained using machine learning. The algorithm may in par- ticular be trained using a training dataset which includes, for one or more persons over one or more exercise activities, the heat flux(es) as well as ground truth data from gas exchange methods (which provides indirect calorimetry data) or from a calorimetric chamber (which provides direct calorimetry data). Optionally, the temperature measure- ments disclosed herein and / or data collected from power meters or other measures of kinetic power output may also be included in the training dataset. The algorithm is trained, using supervised learning approaches using common machine learning tech- niques, to scale the single heat flux value such that the energy expenditure calculated on the basis of the scaled single heat flux value corresponds to the ground truth data. Similar considerations apply to the multiple temperature measurements, which may sim- ilarly be subject to individual scaling, linear combination, and further non-linear scaling of the combined result. In an embodiment, the processor 11 applies a correction to the heat flux HF received from the wearable device 2. Alternatively, the wearable device 2 is configured to apply the correction, and transmit the (corrected) heat flux HF. The heat flux HF is corrected using a heat flux correction term, the heat flux correction term being associated with a defined position on which the wearable device 2, in particular the sensor system, is ar- ranged on the body. Different positions may have different heat flux correction terms. Based on a body position input by the user, for example, the appropriate heat flux cor- rection term may be used. The heat flux correction term may be a multiplicative factor between 0.2 and 5. The heat flux correction term may be determined using calorimetric measurements or indirect calorimetry. The heat flux correction term may additionally be dependent on measured ambient environmental conditions, in particular air temperature P28589PC00 26.05.2025 36 and / or relative humidity, values of which may be received by the processor 11 from ap- propriate sensors. The heat flux correction term may additionally be dependent on clothing worn by the person. In particular, the person may enter or select a clothing type indicator correspond- ing to their worn clothing. The heat flux correction term is then determined based on the clothing type indicator. In an embodiment, the processor 11 applies a correction to the skin temperature ST received from the wearable device 2. Alternatively, the wearable device 2 is configured to apply the correction, and transmit the (corrected) skin temperature ST. The skin tem- perature ST is corrected using a skin temperature correction term, a particular skin tem- perature correction term being associated with a defined position on which the wearable device 2, in particular the sensor system, is arranged on the body. Different positions may have different skin temperature correction terms. Based on a body position input by the user, for example, the appropriate skin temperature correction term may be used In an embodiment, the skin temperature correction term is an offset value of 0.3 °C – 1 °C. The precise value of the offset value depends on the defined position. For example, where the defined position is a chest area of the torso, more particularly an apical loca- tion (located on the left side of the chest between the left armpit and the left hip), the offset value is 0.4 °C – 0.8 °C, preferably 0.5 °C. In an embodiment wherein the defined position is the arm, preferably the upper arm or the wrist, the defined offset value is from between -15 °C to +15 °C, preferably between 0.6 °C – 1.0 °C, more preferably preferably 0.7 °C. The offset value may depend on the clothing worn and / or ambient conditions. P28589PC00 26.05.2025 37 The corrected skin temperature cST is calculated, for example, using the following func- tion: ^^^ = ^^ − ^^^^^^ (2)where ST is the skin temperature and offset is the offset value. In an embodiment, the defined position is selected from one of the following positions: the torso, the upper arm, or the wrist, and the defined correction term is an individual correction term, determined for the particular human. A method for determining the indi- vidual correction term is discussed in more detail with reference to Fig.19. In step S14, the processor 11 calculates a change in the thermal energy in the body. The thermal energy in the body may be represented as a number of Joules of heat stored by the body. The current thermal energy in the body may be determined on the basis of a heat capacity and the measured temperature(s). The heat capacity may be determined using a defined or assumed mass of the person and a specific heat of the person, where the specific heat may be taken to have a standard approximate value of 3 kJ / kg / K for a human body. In particular, the thermal energy (heat energy) in the body at any given point in time may be calculated using the following equation: ^= ^^^ (3)where ^ is the thermal energy in Joules, ^ is the mass of the person in kg, ^ is the spe- cific heat of approximately 3 kJ / kg / K, and ^ is the temperature in Kelvin. The change in the thermal energy may therefore be calculated using the following equation: P28589PC00 26.05.2025 38 ∆^ = ^^∆^ (4)where ∆^ is the change in temperature, in particular a change in the temperature of the person (e.g., skin temperature, core body temperature, or a value derived therefrom). The instantaneous change in thermal energy, or rate of change, may be expressed as a number of Joules per second, i.e. a power, using the following equation: where ^^^is the thermal power, i.e. the power flowing in the thermal capacity, and is the rate of change of the temperature. The change in the thermal energy may be calculated with respect to a baseline thermal energy, where the baseline thermal energy in the body may be calculated on the basis of the body having an assumed baseline temperature, for example of 36.5 °C. The change in the thermal energy in the body may therefore be determined from a single measured temperature value, e.g. the skin temperature. For example, a currently meas- ured temperature may be elevated with respect to the baseline temperature of 36.5 °C, which would result in a currently elevated thermal energy in the body over the baseline thermal energy. The change in the thermal energy may, additionally or alternatively, be calculated be- tween two points in time, specifically using a temperature measured at a first point in time and a temperature measured at a previous point in time. In particular, the difference in temperature may be used to calculate the change in the thermal energy in the body. The two measurements preferably take place on the same day, more preferably within the same (current) activity. The time difference between the measurements is preferably P28589PC00 26.05.2025 39 in the range of 10 seconds to 1 hour. The smaller the time difference, the smaller incre- mental changes in the thermal energy may be determined. The change in thermal energy of the body may be calculated taking into consideration the different heat capacity of, resp. different amounts of heat stored in, the core of the body and the skin of the body, owing to differing specific heats of the core and skin and owing to different temperature dynamics in the skin and core, with the skin experiencing more pronounced temperature variations than the core. In particular, the temperature(s) comprising the core body temperature and the skin temperature may be used to calculate the change in the thermal capacity. The core thermal capacity may be calculated using, or as a function of, a core body temperature, a core body mass, and a core specific heat. The skin thermal capacity may be calculated using, or as a function of, one or more skin temperature measurements, in particular taken at different locations on the body, a skin mass, and a skin specific heat. The particular values for the core body mass and / or the skin mass may be retrieved from memory. For example, the core body mass and / or the skin mass of the person may be retrieved from memory, where it may be stored in conjunction with other user parameters or calculated based on user parameters. For example, the core body mass and / or the skin mass of the person may be calculated based on a known relation (which may be implemented as a table and / or function) and the (total) mass, height, BMI, body fat per- centage, age, and / or sex or the person. For example, the core mass may be calculated as being 80% of the total mass and the skin mass may be calculated as 20% of the total mass. The particular values for the core body mass and / or the skin mass may, additionally or alternatively, also have been determined on the basis of body scanning measurements, P28589PC00 26.05.2025 40 e.g., 3D scans or DEXA scans. The particular values for the core specific heat and the skin specific heat may similarly be taken from known tables. The product of the core mass and the core specific heat, and the product of the skin mass and the specific heat, may alternatively also be determined experimentally using a method as described herein. In particular, the following equation may be used to determine the thermal energy in the body: ^= ^^^^^^^^^^^^^^^ + ^^^^^^^^^^^^^^^ (6)where ^^^^^, ^^^^^, and ^^^^^are the core mass, core specific heat, and core tempera- ture, respectively, and ^^^^^, ^^^^^, and ^^^^^are the skin mass, skin specific heat, and skin temperature, respectively. The change the thermal energy may be calculated using the following equation: ∆^ = ^^^^^^^^^^∆^^^^^ + ^^^^^^^^^^∆^^^^^ (7)and the instantaneous change may be calculated using the following equation: where ^^^is the thermal power entering or leaving the body, thereby either increasing or decreasing the heat energy stored in the body. Alternatively, the symbol ^̇ may be used to denote the heat transfer rate into or out of the body. P28589PC00 26.05.2025 41 In step S15, the processor 11 calculates a rate of energy expenditure of the person. The rate of energy expenditure may be expressed as a power, i.e. Watts or Joules per second expended by the person. The rate of energy expenditure is, in other words, indicative of, related to, or a component of the total calories being burned by the person. The rate of energy expenditure is calculating using the heat flux and the change in the thermal en- ergy of the body. In particular, the rate of energy expenditure may be calculated as a function of the heat flux and the change in the thermal energy in the body, wherein the function is preferably a sum of the outward heat flux and the increase in the thermal energy. For example, the following equation may be used to determine the rate of energy ex- penditure: ^^^ = ^^^^^ + ^^^ (9)where ^^^is the rate of energy expenditure (power) expressed in Watts, ^^^^^is the rate of heat lost through the skin as determined using the measured heat flux, and ^^^is the rate of change in the thermal capacity of the body, i.e. the change in the heat energy stored in the body. Additionally, a kinetic power term produced by the person may be included in the deter- mination of the rate of energy expenditure. The kinetic power may be estimated basedon ^^^^^ + ^^^, for example as 0.25 × (^^^^^ + ^^^).In an embodiment, the heat flux used to calculate the rate of energy expenditure is a total heat flux, calculated using the heat flux and a pre-defined body surface area factor. The body surface area factor is indicative of the total body surface of the person. The body surface area factor may be retrieved from memory, having been entered via user P28589PC00 26.05.2025 42 input. The body surface area factor may be included in one of the stored user parame- ters. The body surface area factor may be calculated using a known relation (e.g., a table and / or a function) using of one or more other physical characteristics of the person re- trieved from memory, in particular stored user parameters including a body mass, a height, a body-mass index (BMI), a body fat percentage, a sex, and / or an age. For ex- ample, the body surface area factor may be calculated using a body surface area ac- cording to the empirically derived formula of Du Bois and Du Bois, in which the bodysurface area is computed as follows: ^^^ = ^^.^^^ × ℎ^.^^^ × 0.007184, where ^^^ isthe body surface area in square meters (^^), ^ is the mass in kilograms, and ℎ is the height in centimeters. The body surface area factor may be the measured or calculated body surface area in square meters. The body surface area factor may additionally or alternatively be defined based on meas- urement results, for example body scanners, DEXA scans, etc. The heat flux measurement ^^^^^by the heat flux sensor may be provided in the units of Watts per square meter. By multiplying with the body surface area factor, the total Watts or power loss ^^^^^through the skin may be determined. For example, the following equation may be used to determine the rate of energy ex- penditure: ^^^ = ^^^^^ × ^^ + ^^^ (10)where ^^^is the rate of energy expenditure (power) expressed in Watts, ^^^^^is the rate of heat lost through the skin per square meter as determined using the measured heat flux, ^^ is the body surface area factor in square meters, and ^^^is the rate of change P28589PC00 26.05.2025 43 in the thermal capacity of the body, i.e. the change in the heat energy stored in the body. The heat flux term ^^^^^may be multiplied by the heat flux correction term (typically be- tween 0.2 and 5, depending on the body position where the heat flux measurement is performed). Additionally, the kinetic power term as described above may be included. In an optional step S16, the processor 11 generates a message including the rate of energy expenditure. The message may be recorded in the memory 12. The message may also be transmitted back to the wearable device 2, to the user device 2, and / or to the server computer 6. The message may be transmitted only if the rate of energy ex- penditure exceeds a pre-defined rate threshold. The message may include the rate of energy expenditure expressed in one or more of a plurality of formats or representations, including numerical, descriptive, or even colour- based. For example, the rate may be expressed in a power (Watts), i.e. Joules per sec- ond, or kilo-calories per hour. The message may further include an alarm, warning, and / or alert, depending on the value of the rate of energy expenditure. The message may be configured such that it is displayed as an important notification on the user device 4, for example. The message may be configured to be displayed prominently, and may include the use of signal colors, i.e. conspicuous colors such as orange or red that have a signal effect and which are interpreted by a substantial proportion of humans as a warning signal. In an embodiment, the electronic system 1 is configured to display the message on a display, for example a display 23 of the wearable device 2, and / or on a display 41 of the user device 4. P28589PC00 26.05.2025 44 Fig.12 shows a flow diagram illustrating a method 120 including a number of steps S13 – S15 which are described above with reference to Fig.11, as well as further steps S17 to S19. As depicted in the flow diagram, the steps S13 – S15 are performed continuously, for example once every second or once every ten seconds. In step S17, the rate of energy expenditure calculated in step S15 is used to determine, in the processor 11, a cumulative energy expenditure. The cumulative energy expendi- ture is an indicator or measure of a caloric deficit of the person during a defined time period between two time-points, in particular a time period of monitoring the rate of en- ergy expenditure (for example a time point of starting a current or past exercise activity). The cumulative energy expenditure can be a useful indicator for purposes of monitoring a caloric deficit (representative of a total calorie loss during exercise, taking into account any calories consumed during exercise), for example to ensure that the caloric deficit is not too small, too large and / or lies within a defined target range, to ensure fueling during and / or after the exercise activity is adequate to replenish, either completely or in part, the total calories burned. The cumulative energy expenditure may be a valuable figure not only for athletes and their coaches, but also for dieting. The cumulative energy expenditure may be calculated “live”, that is, calculated and pref- erably continually updated during a current monitoring period, in particular during a pe- riod of activity. The cumulative energy expenditure may be calculated using a current value of the rate of energy expenditure and a duration of the monitoring period. Prefera- bly, the rate of energy expenditure is calculated using one or more past values of the rate of energy expenditure during the current monitoring period. The cumulative energy expenditure may also be calculated retrospectively, that is, cal- culated subsequent to the monitoring period (e.g., exercise activity) based on a plurality P28589PC00 26.05.2025 45 of values of the rate of energy expenditure calculated using (and / or recorded during) the heat flux and the temperature(s). The cumulative energy expenditure may be calculated as a function of the average value of the rate of energy expenditure during the monitoring period (or part thereof) and a duration P between two defined time-points t1 and t2 of the monitoring period (or part thereof). The duration P may be the entire monitoring period, a duration P up to the current present moment, or a subset of the entire period. The duration P may also be selected as an entire day, for example. The cumulative energy expenditure may be calculated using the following equation: ^^ ^= ^ ^^^^^ (11) ^^ where ^^^is the rate of energy expenditure as calculated herein, for example using equation 10, and ^1 and ^2 are two defined time-points. The defined time-points may be, for example, a time-point corresponding to the beginning of an exercise activity and a current time-point. The defined time-points may correspond to the beginning and end of an exercise activity, or the beginning and end of a whole day, for example. In the optional step S18, the processor 11 generates a message including the cumulative energy expenditure. The message may be recorded in the memory 12. The message may be transmitted to the wearable device 2, for example for displaying on the display 23 of the wearable device 2. The message may include the cumulative energy expenditure, for example as a numer- ical value. Alternatively or additionally, the message may include a representation of the P28589PC00 26.05.2025 46 cumulative energy expenditure, for example a text, color, or audio signal which depends on the cumulative energy expenditure. The message may also be transmitted back to the wearable device 2, to the user device 4, and / or to the server computer 6. The message may be transmitted only if the cumula- tive energy expenditure exceeds a pre-defined cumulative energy expenditure threshold. The threshold may be, for example, defined as 500 calories. The transmission of the message may also depend on a time, e.g., a time since a last notification was sent. For example, the message may be sent only at defined time intervals (e.g., every 20 minutes). The message may further include a prompt or notification including instructions, e.g., written instructions, to consume nutrition. The prompt to consume nutrition may be gen- eral or specific. A specific prompt may include details as to how much nutrition is to be consumed, for example a number of grams of carbohydrate and / or a number of calories to consume. The prompt may also be configured to indicate to the person particular types of products to consume, e.g., an energy gel, a sports drink, or a sports bar. The prompt may include identifiers of particular products to be consumed. In the optional step S19, the processor 11 receives a response message from the user, for example via a user device. The response message is indicative of the user having fueled, i.e. consumed calories in the form of solid, gel, and / or liquid nutrition. The mes- sage is in particular indicative of a particular caloric amount consumed. The processor updates the cumulative energy expenditure accordingly and / or may calculate or maintain a separate value indicative of a current caloric deficit based on the cumulative energy expenditure and consumed calories. The current caloric deficit may be particularly useful during long activities such as bicycle racing, triathlon, marathon running, etc., as it pro- vides the person with a current measure of their caloric loss and allows the person to P28589PC00 26.05.2025 47 ensure that their calorie consumption is sufficient to cover their cumulative energy ex- penditure. Fig. 13 shows a flow diagram illustrating a method 130. The method 130 includes a number of steps S131 to S134. The method 130 may be performed by the electronic system. Steps S131 and S132 are analogous to steps S13 and S14 described in detail above with reference to methods 110 and 120. The method 130 may be performed in addition, or as an alternative, to the methods 110 and / or 120. Likewise, certain steps shown in method 130 may be used in the methods 110 and / or 120, in particular inserted in between existing steps or used to replace existing steps. In particular, step S133 may be inserted into the methods 110 and / or 120 prior to step S15, and step S134 may re- place step S15. The method 130 in particular calculates the rate of energy expenditure takes into account a further factor in the energy expenditure of the person, specifically a kinetic power pro- duction of the person, to more accurately calculate the energy expenditure. In step S133, a measure of a kinetic power output of the person is received in the elec- tronic system. The kinetic power output of the person is the amount of useful mechanical energy produced by the person. The useful mechanical energy is that which the person exerts against their environment in the course of performing a physical activity. For ex- ample, the kinetic power output of a cyclist is the power being imparted by the cyclist into the pedals. The kinetic power output of a rower on a rowing machine relates to the power with which the person pulls the handle of the rowing machine. The measure of the kinetic power output may be based on a more direct measurement of the kinetic power output, for example as measured by an ergometer such as are known for bicycles, rowing machines, etc. These ergometers directly measure the force or P28589PC00 26.05.2025 48 torque applied over a particular period of time and thereby can calculate the power pro- duced by the person. The measure of the kinetic power output may be based on a more indirect measurement of the kinetic power output, for example using motion sensors (including, for example, accelerometers, gyroscopes) to calculate a running or a swimming power, or using sat- ellite based location to determine speed over terrain and thereby estimate the kinetic power output. Another example of an indirect measurement of a kinetic power output may be based on heart rate. These techniques of measuring or estimating the kinetic power output are established and known. The measure of the kinetic power output of the person is received in the electronic sys- tem from a sensor or device integrated into the electronic system and / or communicatively coupled to the electronic system. For example, the kinetic power output may be received in the electronic system from a cycling power meter via a Bluetooth low energy (BLE) or ANT+ signal. In step S134, the rate of energy expenditure is calculated using the heat flux HF (in particular, the total heat flux), the change in the thermal energy, and the kinetic power output. For example, the rate of energy expenditure is calculated using the following equation: ^^^ = ^^^^^ + ^^^ + ^^ (12)where ^^is the kinetic power output. ^^^^^may be corrected using the body surface area factor as is described above with reference to Equation 10. P28589PC00 26.05.2025 49 In an embodiment, the kinetic power output and / or another measure of exercise intensity, such as a measured breathing rate or heart rate, may additionally be used to provide more precise fueling instructions. This is because the relative exertion of the person has an influence on the energy sub- strate balance used by the body of the person. More specifically, the relative exertion influences how much energy the body produces from fat stores in relation to carbohy- drate stores. For example, at relatively low intensities (zone two in the five or seven zone performance model), the body predominantly burns fat as a fuel source rather than car- bohydrates. At higher intensities, the energy demands of the body increase beyond what burning fat can provide, and the body begins burning a larger ratio of carbohydrates vs. fat. Therefore, it is beneficial for fueling instructions to take into consideration the current relative exercise intensity of the person, in particular by calculating a current caloric con- sumption of carbohydrates and providing fueling instructions based only on the propor- tion of caloric consumption of carbohydrates and not fats. As the fat stores in a typical person may be assumed to be very large and functionally non-exhaustible during a single exercise activity, the reduction in the fat stores do not need to be considered when cal- culating the caloric deficit for the purposes of refueling during the activity. On the other hand, maintaining adequate carbohydrate stores may be critical for exercise perfor- mance, in particular in events with a duration of longer than one hour, as the human body cannot store more than a couple of hours’ worth of carbohydrates and exercise perfor- mance may deteriorate dramatically if the person does not refuel properly during the activity. Specifically, the method comprises calculating the caloric deficit of the person using the cumulative energy expenditure during a defined period of time and a measure of exercise intensity. P28589PC00 26.05.2025 50 The caloric deficit may be indicated, for example, as a number of kilocalories. The caloric deficit, however, may additionally be indicated as an amount of fat (e.g., in grams) and / or carbohydrates (e.g., in grams). These additional considerations when calculating the caloric deficit may be used, for example, in conjunction with step S18 of method 120 described herein. The measure of exercise intensity may be defined using the received kinetic power out- put (directly and / or indirectly measured) of the person and a pre-defined performance profile of the person, wherein the pre-defined performance profile includes a mapping of kinetic power output to one or more performance zones, each performance zone related to a particular energy substrate balance indicative of a proportion of fats burned to car- bohydrates burned. The pre-defined performance profile of the person may be retrieved from memory and may be included in user parameters entered during setup. The pre-defined performance profile may be defined on the basis of a single number, for example a functional threshold power (FTP) or the like. The measure of exercise intensity may also be determined on the basis of one or more of: a received heart rate measurement, a received lactate measurement, and / or a breath- ing rate measurement, and a pre-defined performance profile, wherein the pre-defined performance profile includes a mapping of one or more of: a received heart rate meas- urement, a received lactate measurement, and / or a breathing rate measurement to one or more performance zones, each performance zone related to a particular energy sub- strate balance indicative of a proportion of fats burned to carbohydrates burned. The pre-defined performance profile may be based on a pre-defined default performance profile based on standard table values or calculated on the basis of the user settings P28589PC00 26.05.2025 51 stored in memory, or a pre-defined individual performance profile retrieved from memory, which may have been stored in memory as part of the user settings. In an embodiment, received responses from the user relating to the user’s fueling, for example as described herein with reference to step S19 of method 120, are taken into account when determining the energy substrate balance. In particular, recent refueling may increase the proportion of carbohydrates burned vs. fat, due the ready availability of sugars entering the bloodstream from the digestive tract, and therefore the energy substrate balance may take this into account by increasing the carbohydrate vs. fat bal- ance depending on the current caloric deficit and / or the number of calories (in particular calories of carbohydrates) consumed in a defined period, for example within the last 120 minutes. Fig. 14 shows a flow diagram illustrating a method 140. The method 140 includes a number of steps S141 to S144. The method 140 may be performed by the electronic system. Steps S141 and S142 are analogous to steps S13 and S14 described in detail above with reference to methods 110 and 120. The method 140 may be performed in addition, or as an alternative, to the methods 110, 120, and / or 130. Likewise, certain steps shown in method 140 may be used in the methods 110, 120, and / or 130, in partic- ular inserted in between existing steps or used to replace existing steps. In particular, step S143 may be inserted into the methods 110 and / or 120 prior to step S15, and step S144 may replace or augment step S15. The method 140 in particular calculates the rate of energy expenditure takes into account a further factor in the energy expenditure of the person, specifically a respiratory power production of the person, to more accurately calculate the energy expenditure. P28589PC00 26.05.2025 52 The respiratory power loss is due to the exhalation of warm, moist air. In particular, the change in the thermal energy due to exhaled air being warmer and more humid than inhaled air is taken into account to more accurately calculate the rate of energy expendi- ture. In step S144, the respiratory thermal energy loss (or respiratory heat loss) is received and / or calculated. The respiratory thermal energy loss may be received from an external device which per- forms a measurement on the inhaled and / or exhaled gasses of the person, for example a spirometer. The respiratory thermal energy loss may additionally or alternatively be calculated using the heat flux through the skin, the rate of change of the thermal energy in the body, and a respiratory heat loss factor. For example, the respiratory thermal energy loss may be calculated using the following equation: ^^ = (^^^^^ + ^^^ ) × ^^ (13)where ^^is the rate of respiratory heat loss in Watts, and ^^ is the respiratory heat loss factor. Optionally, the kinetic power ^^may be included in equation 13, in particular as a further summand scaled by the respiratory heat loss factor ^^. The respiratory heat loss factor ^^ may be assumed to be 0.1, however, depending on ambient conditions (i.e. ambient temperature and / or relative humidity), the respiratory heat loss factor may deviate from 0.1. Under typical ambient conditions, it may be as- sumed that the person inhales semi-dry air with a relatively low relative humidity and exhales warm air with a relatively high relative humidity (e.g., up to 100% relative humid- ity). The person therefore loses water during exhalation which requires a phase change P28589PC00 26.05.2025 53 to occur in the lungs as the water evaporates. The majority of the respiratory heat loss factor is due to the heat of evaporation of the water. The respiratory heat loss factor may be determined more accurately by receiving, from a sensor either integrated into elec- tronic system, or external to the electronic system, an ambient temperature and / or an ambient relative humidity. Additional variables and parameters may also be taken into account, in particular a current breathing rate of the person and a current tidal volume of the person. The breathing rate and / or tidal volume may be estimated, based on a measure of relative exertion determined using, for example, the heart rate or the kinetic power produced. Specifically, a defined relation, for example in the form of a data table and / or a para- metrized model, may be used to map a current heart rate to a current (assumed) breath- ing rate. The relation may be piece-wise linear. The tidal volume may be determined using defined a lung volume of the person, the breathing rate and / or the relative exertion. The data lung volume of the person may be determined on the basis of their gender, height and / or weight, or on the basis of an em- pirically determined lung volume defined as part of the user parameters by the person. Relations between breathing rate, tidal volume and exertion are known in the literature, for example from Blackie, et al. (1991). Normal Values and Ranges for Ventilation and Breathing Pattern at Maximal Exercise. Chest, 100(1), 136–142. doi:10.1378 / chest.100.1.136. The breathing rate and / or tidal volume may be measured or more directly inferred from sensor signals. For example, the signal from a PPG sensor is weakly modulated by the breathing rate. Appropriate low-pass filtering on the PPG sensor may therefore be used P28589PC00 26.05.2025 54 to determine the breathing rate. Alternatively or additionally, a chest strap sensor de- signed to measure the expansion and contraction of the chest strap may be used to determine the breathing rate and / or the tidal volume. Specifically, the breathing rate may be determined using the periodicity / frequency of the expansion and contraction of the chest strap, while the tidal volume may be inferred from the amplitude of the expansion and contraction, preferably including a defined or estimated height, weight, sex, and chest circumference of the person. The rate of heat loss ^^due to respiration may be determined by subtracting the heat content in the inhaled air from the heat content in the exhaled air. In particular, the heat content in the inhaled air is calculated as a function of the ambient air temperature, the ambient relative humidity, the breathing rate and the tidal volume, while the heat content in the exhaled air is calculated as a function of the exhaled air temperature (may be assumed to be 38 °C) and the exhaled relative humidity (may be assumed to be 100%), the breathing rate and the tidal volume. Thereby, the rate of heat loss ^^may be derived. directly, forgoing the need to estimate a respiratory heat loss factor ^^. For example, at 20 °C and 40% relative humidity, the water content of inhaled air is about 7 mg / L. The water content of inhaled air is typically in the range of 3 mg / L to 25 mg / L (which corresponds to 10 °C at 30% relative humidity and 30 °C and 80% relative hu- midity, respectively). The water content of exhaled air is approximately 42 mg / L (38 °C and 100% relative humidity). Therefore, the water loss via breathing is typically in the range of 20 – 40 mg per liter of exhaled air. A water loss, within this range, of 30 mg / L during medium intensity exercise (breathing rate at 40 breaths per minute and tidal vol- ume at 2 liters of air per breath) therefore results in a loss of 40 mg of water per second. By taking into account the heat of vaporization of water of 2.26 J / mg, the reate of heat loss ^^is 90 Watts. P28589PC00 26.05.2025 55 In an embodiment, one or more further physiological signals are received and used to refine the calculation of the rate of energy expenditure. The physiological signals include those physiological signals which vary due to the rate of energy expenditure. The phys- iological signals include, for example, heart rate, heart rate variability, and / or respiration rate (i.e. breathing rate). The physiological signals may further include a galvanic skin response, hydration status, body weight, a sweat rate, a salt and / or electrolyte concen- tration in sweat, a perfusion, and / or other aspects of electro dermal activity. Fig.15 shows a flow diagram illustrating a method 150 for determining the correction term for a particular individual, the correction term being used to correct the skin temper- ature ST as described herein. The defined correction term relates in general to a heat transfer coefficient between the skin and the environment, which varies across the skin surface and whose variation is different from individual to individual. The correction term determined hereby takes into account differences between individuals and provides and may further take into account clothing worn over the wearable device 2, in particular over the skin temperature sensor 32 of the sensor system 3. The method allows for correction terms to be determined for different defined positions. In particular, the method is used to find the correction term for the apical position, i.e. the position on the left side of the chest indicated by reference numeral 81 in Fig 1. The method 150 includes a number of steps S151 – S155. The steps may partly or wholly be performed in the processor 11, partly or wholly in the wearable device 2, or in conjunction between the processor 11 and the wearable device 2. Additionally, the user device 4 and / or the server computer 6 may also perform part or all of one or more of the steps S151 – S155. In a preparatory step, three or more, preferably four, skin temperature sensors 32 are attached to the body 8 of the person. The skin temperature sensors 32 are, for example, attached at defined positions on the body 8 of the human, in particular using a selection of the defined positions 81, 82, 83, 84, 85 as depicted in Fig.1. The three or more skin P28589PC00 26.05.2025 56 temperature sensors 32 preferably communicate wirelessly with the wearable device 2 and / or a user device 4. The measured skin temperatures may be transmitted, from the skin temperature sensors 32 directly, or via an intermediary device, to the processor 11. In step S151, three or more skin temperature measurement values are received from the three or more skin temperature sensors 32. The three or more skin temperature meas- urement values will not all be identical, as the sensors are placed on different parts of the body 8 which have a different skin temperature. In step S152, an average (e.g., a mean) skin temperature value is calculated using the three or more skin temperature measurement values. The average skin temperature aST may be calculated using the following formula: wherein the subscript of the skin temperature ST indicates the position 81, 82, 83, 84 on the body 8. In step S153, the instantaneous correction term is calculated using the current value of the average skin temperature aST. The instantaneous correction term iCT is calculated for example as a difference between the desired defined position (e.g., the apical position 81) and the average skin temperature aST using the following formula: ^^^ = ^^^^ − ^^^ (15)The instantaneous correction term iCT is recorded. As indicated in Fig.15, steps S151 – S154 occur repeatedly for a particular duration of time, for example for the duration of P28589PC00 26.05.2025 57 a first heat training session. The instantaneous correction term iCT is recorded for the duration and then the correction term CT is derived therefrom. In step S154, the correction term CT is determined using the recorded values of the instantaneous correction term iCT. The correction term CT may be determined using one or more averages (e.g., mean, median, and / or mode) of the instantaneous correction term iCT. In step S155, the correction term CT is recorded in the electronic system 1. For example, the correction term CT is recorded in the memory of the wearable device 2 and / or in the memory 12 connected to the processor 11. The method as described above therefore enables the electronic system 1 to apply, in future periods of elevated heat, an individualized correction term CT to measurements of the skin temperature taken at the defined position, for example the apical position 81. Fig.16 shows a flow diagram illustrating a method 160 which may be used to set up and initialize a user device such that it may perform one of the methods as described herein. The method is typically initiated by the user (person) and needs to be performed only once. The method 160 includes a number of steps S161 – S163. The method 160 is performed by the electronic system, in particular a user device 4 (e.g., a smart phone or activity tracker such as a smart watch or cycling computer) or a wearable device 2 (e.g., a smart watch) as described herein, in particular with reference to Figs.2 to 8. In step S161, the electronic system installs software, i.e. computer program code, con- figured to perform the one or more methods described herein. The software may be in the form of an application (App) and / or library. The software may include interfaces to communicate with a remote server to perform at least some of the methods and / or steps as described herein, i.e. the software may comprise a client and server architecture. P28589PC00 26.05.2025 58 The software may be installed based on user input. The software may be downloaded, for example from an online server such as App store. For example, the user may down- load and install an App from an online App store onto his user device, in particular onto the memory. The software may also be installed onto a wearable device which may have a direct connection to a remote computer or server computer as suggested in Fig.8, or an indirect connection as suggested in Fig.7. In step S162, the user runs the software on the user device and / or on the wearable device and configures the software, for example by entering settings and / or user param- eters. The settings and / or user parameters are stored in the memory. They may addi- tionally or alternatively be uploaded to a remote server. For example, the user may enter settings including fueling parameters, such as how often to send messages (e.g., notifications) and based on which preferences (frequency of notification, notification after a defined time period, etc.). The user may also enter particular nutrition available, such that the methods described herein may take into ac- count the particular nutrition available when notifying the user to fuel, particular foods, gels, and / or beverages. The user may additionally enter user parameters, such as a weight, height, body mass index, body fat percentage, age, sex, etc. which may be used to determine correction terms and factors as described herein. In step S163, the user may pair the user device or the wearable device with the sensor(s) using a known pairing mechanism, for example using Bluetooth pairing. The user may be asked to input a body position where the sensor(s) are located, which locations are then stored in the memory. Multiple sensor systems may be paired, each located at a different positions on the users body. P28589PC00 26.05.2025 59 Fig.17 shows a flow diagram illustrating a method 170 for performing one or more of the methods described herein. The method 170 comprises a number of steps S171 – S172. The method 170 may be initiated by the user and performed on demand. The method 170 may be performed subsequent to the method 160 in which the user device is pre- pared and initialized by installing the appropriate software. In step S171, the user (person) activates the user device and / or the wearable. For ex- ample, the user powers on the user device and / or the wearable. Depending on the user device, the software necessary to perform the methods described herein may be launched automatically with the startup of the user device and / or the wearable. For ex- ample, if the user device is a smart phone, the software may be launched on startup of the device or launched by executing the appropriate App. If the user device is an activity tracker, such as a smart watch or cycling computer, the software may launch automati- cally when an activity is started or the device is powered on. In step S172, the user provides a user input into the user device to start the activity. This step may be skipped if the user device is configured to launch the software automatically and / or start the activity as soon as the software is launched or the user device is powered up. Once activity tracking has started, the user device and / or the wearable device receives the heat flux temperature(s) from the sensor system and begins calculating the rate of energy expenditure as described in the methods herein. Depending on the embodiment, the user device and / or the wearable device may store the (raw) received measurement data and / or the calculated rate of energy expenditure. The user device and / or the wear- able device may also begin calculating and updating the cumulative energy expenditure as described herein. The cumulative energy expenditure is preferably calculated for a time interval from a time-point at which the activity started and a current time point. P28589PC00 26.05.2025 60 In step S173, the message indicative of energy expenditure (comprising the rate of en- ergy expenditure and / or the cumulative energy expenditure) is displayed on a display as described herein. Thereby, the person receives information relating to their energy ex- penditure. In optional step S174, a message including fueling instructions is displayed on a display as described herein. The contents of the message may be combined with the contents of the message of step S173. Thereby, the person receives information relating to their cumulative energy expenditure and / or their current caloric deficit. The user may provide user input into the user device and / or wearable device after to consuming fuel (i.e. eating or drinking). The input may indicate or specify nutritional con- tent of the consumed fuel, for example by indicating a product consumed (e.g., energy bar or energy gel) and / or an amount of carbohydrates or calories consumed. The user device may then take into account the consumed calories for updating a caloric deficit of the user (person), wherein the caloric deficit is calculated as difference between the cu- mulative energy expenditure and the total consumed calories. The caloric deficit may be tracked and also displayed to the user alongside or instead of the cumulative energy expenditure. In step S174, the activity ends. The activity may be ended based on user input into the user device and / or wearable device. The activity may also be ended by terminating the software and / or powering down the user device. After the activity has ended, the cumu- lative energy expenditure for the duration of the entire activity may be calculated and displayed. Depending on the embodiment, activity data, which may include the recorded sensor measurements and any values calculated using the sensor measurements, for example P28589PC00 26.05.2025 61 the rate(s) of energy expenditure, the cumulative energy expenditure, and / or the total caloric deficit, may be transmitted, by the user device, to a remote server for logging or archival purposes or such that the user and / or a coach may evaluate the activity data and, for example, recommend a refueling plan for example including nutrition to con- sume. Fig.18 shows a chart illustrating the heat flux through the skin as a function of time for most of a day, the day including an exercise activity (workout). Additionally, two com- mutes are also shown, which commutes were performed by bicycle. The chart shows that using the heat flux alone for providing a measure of the energy expenditure is insufficient to provide the person with live or real-time feedback on their energy expenditure, as it lags behind the actual energy expended during the activity. As can be seen in the chart, the heat flux is non-zero due to a baseline energy expendi- ture of the human body, even when at rest, which amounts to approximately 2000 kcal per day for an average person. The chart illustrates how the heat flux rises slightly during a commute to work by bicycle and also rises in the evening during a second commute home from work. During the day, an activity is recorded. The activity starts at the time-point t1 and ends at the time-point t2. As shown in the chart, the heat flux rises from the baseline in a substantially steady manner after begin of the activity until, after some time (e.g., approx- imately 20 minutes), the heat flux reaches a plateau. This is an initial warm up period during which the exercise intensity gradually increases and therefore the heat flux also gradually increases. After the warm up, the heat flux remains roughly constant. The ex- ercise activity ends at the time-point t2 and while the exercise intensity reduces sharply to zero, the heat flux only gradually decreases during a post-exercise cool-down period P28589PC00 26.05.2025 62 to return to baseline. During the post-exercise cool-down period, the person’s core body temperature gradually decreases and therefore the heat flux through the skin remains elevated above baseline. Fig. 19 shows a flow diagram illustrating a method 190 for determining the heat flux correction term. The method 190 may be performed as a form of personal calibration in order to determine a personal heat flux correction term. The method 190 is performed by the electronic system, for example by the user device. The method 190 may addition- ally or alternatively be performed by a remote server. The method 190 comprises a num- ber of step S191 to S195. The method 190 is preferably performed after an exercise activity and uses the cool down phase where the body of the person returns to a baseline temperature and there- fore also thermal capacity. As is explained below in more detail, the heat flux correction term may be calculated by comparing, during a cool down period of a defined period of time, the change in the thermal energy stored in the body with the heat flux through the skin. In step S191, energy expenditure data during a post-exercise time-period is received, for example from memory. The energy expenditure data may comprise the rate of energy expenditure during the post-exercise time-period. The energy expenditure data may comprise the cumulative energy expenditure during the post-exercise time-period between time-points t0 (which may correspond to the end of the exercise activity) and t1 (which corresponds to a time- point where the body has substantially returned to a baseline thermal capacity or base- line temperature(s). P28589PC00 26.05.2025 63 The energy expenditure data may comprise measurements used to calculate the rate of energy expenditure and / or the cumulative energy expenditure, for example one or more measurements taken during the post-exercise time-period which are indicative of a measure of the thermal energy stored in the body of the person, such as temperature measurements. Additionally, a heat capacity, or equivalently a mass and a specific heat, of the person may be used. In an embodiment, the core mass, core specific heat capacity, and one or more core temperatures, along with the skin mass, skin specific heat capacity, and one or more skin temperatures are retrieved from the energy expenditure data and / or from user pa- rameters. Additionally, further recorded data, for example relating to the kinetic power output, movement or motion data and / or further recorded physiological signals relating to heart rate, for example, is received, for example from the memory. In step S192, a post-exercise time-period is determined. The post-exercise time-period is a period between time-points t0 (which may correspond to the end of the exercise activity) and t1 (which corresponds to a time-point where the body has substantially re- turned to a baseline thermal capacity or baseline temperature(s). The post-exercise time-period may be determined by the user, in particular the user may enter the time-points t0 and t1, for example after consulting a chart illustrating the energy expenditure data. The post-exercise time-period may be determined using the energy expenditure data, for example by identifying a first time-point t0 as a time-point after which at least one of the temperature(s) and / or the heat flux as recorded in the energy expenditure data de- clines, preferably following substantially an exponential decline. The decline may further P28589PC00 26.05.2025 64 be identified by calculating a moving average of the temperature(s) and / or the heat flux, and the time-point t0 is identified as a point where the moving average decreases below a defined threshold. The first time-point t0 may also be determined using the kinetic power output, in particular as a time-point where the kinetic power output drops to zero, or substantially to zero. Similar considerations apply to movement or motion data. The second time-point t1 may be identified as a time-point subsequent to t0 at which the temperature(s) and / or the heat flux has returned to their baseline values or within a small defined margin of the baseline values (e.g., to within 0.2 °C for the temperature, or to within 10 W / m2 for the heat flux). The second time-point t0 is typically found between 20 and 60 minutes post exercise. A positive identification of the second time-point t1 may further require that the temper- ature(s) and / or the heat flux have a monotonous decline during the post-exercise time- period, and / or that the kinetic power output and / or movement or motion data is indicative that no exercise is taking place (i.e. the person is substantially at rest), and / or further physiological signals are also returning to their baseline values. In step S193, the change in the thermal energy stored in the body is calculated in the post-exercise time-period. used to determine the change in the thermal energy in the body as described herein in more detail. The change in the thermal energy stored in the body during the post-exercise time-period may be calculated using the following equation: P28589PC00 26.05.2025 65 ∆^ = ^^∆^ (16)as described above, or, alternatively, the following equation: ∆^ = ^^^^^^^^^^∆^^^^^ + ^^^^^^^^^^∆^^^^^ (17)where ∆^ = ^(^0) − ^(^1) and more specifically ∆^^^^^ = ^^^^^(^0) − ^^^^^(^1) and∆^^^^^ = ^^^^^(^0) − ^^^^^(^1).Because of the conservation of energy, the decrease in the thermal energy stored in the body during the post-exercise time-period must be accounted for by the energy leaving the body, which predominately occurs via heat flowing through the skin to the environ- ment. In step S194, the heat flowing through the skin to the environment which is related to the decrease in the thermal energy in the body is calculated. However, because only the decline in the excess thermal energy is relevant, i.e. the additional thermal energy stored in the body due to activity, the same considerations apply when dealing with the heat flux, in that only the excess heat flux is of interest. The total excess thermal energy flow ^^^^^in Joules through the skin during the post- exercise time-point may be calculated as a sum or integral over the excess heat flux through the skin during the post-exercise time-point. In other words, the baseline heat flux must not factor into the calculation. The total excess thermal energy flow ^^^^^through the skin during the post-exercise time-point may therefore be calculated using the following equation: P28589PC00 26.05.2025 66 where ^^ is the body surface area factor, given in square meters, ^^^^ is the unitless heat flux correction term, and ^^^^^(^) is the heat flux in Watts per square meters. The term ^^^^^(^1) is subtracted to account for the baseline heat flux such that the integral is over the excess heat flux. In step S195, the heat flux correction term HFCT is calculated using the change in the thermal energy stored in the body during the post-exercise time-period and the total ex- cess thermal energy flow through the skin during the post-exercise time-point. Specifi- cally, the heat flux correction term HFCT may be calculated by equating ∆^ and ^^^^^and solving for ^^^, in particular using the following equation: Subsequently, the calculated heat flux correction term HFCT may be stored in the memory, preferably as part of the user parameters. The heat flux correction term HFCT may be used in one or more of the methods described herein to more accurately deter- mine the energy expenditure. Preferably, the heat flux correction term HFCT is assigned or associated with a particular body position at which the sensor system, in particular the heat flux sensor, was worn during the cool-down period. Thereby, when wearing the sensor system at the same or a comparable position during subsequent activities, the heat flux correction term HFCT can be used to provide more accurate heat flux measurements, respectively to deter- mine, using the measured (local) heat flux, the total heat flux through the body. By using the heat flux correction term HFCT, it is also possible to use a roughly calcu- lated value for the body surface area factor SA computed from mass and height alone P28589PC00 26.05.2025 67 and using the heat flux correction term HFCT to account for any discrepancies between the computed body surface area factor SA and the actual body surface area. In an embodiment, the body surface area factor SA term is combined with the heat flux correction term HFCT and the method 190 is used to calculate the product of the body surface area factor SA (which may be designed the value of one square meter, for ex- ample) and the heat flux correction term HFCT, thereby forgoing any need to calculate the body surface area factor SA specifically. Fig.20 shows six time-series charts (a – f) relating to an exemplary exercise activity performed by a person. The charts include raw measurement data, as well as various values and data determined therefrom using one or more of the methods described herein. The first ten minutes of the time-series relate to an initial baseline period where the person is at rest. The exercise activity takes place between the start time-point t0 at ten minutes and the end time-point t1 at fifty minutes. After the end of the exercise activity at t1, the person returns to rest. Chart (a) shows the metabolic power, as measured using spirometry, as well as the ki- netic power produced by the person, measured using a power meter. As shown, the kinetic power produced during the exercise is, after a short ramp up period, a steady 200 W. The total metabolic power is approximately 1100 W. Chart (b) shows the rate of heat loss through the skin as measured using a heat flux sensor as described herein. It can be seen that the rate of heat loss increases shortly after exercise onset to a first value of around 1000 W, then rises further during the sec- ond half of the exercise activity to value of around 1200 W. After t1, the rate of heat loss drops back down towards the baseline. P28589PC00 26.05.2025 68 Chart (c) shows the skin and core body temperature as measured by a skin temperature sensor and core temperature sensor, respectively. As shown, the core body temperature is initially approximately 37 °C but rises during the exercise activity to above 38 °C. After t1, the core body temperature drops back to the baseline. The skin temperature, on the other hand, is initially around 33 °C, rising to a first value of above 34 °C before rising further to a peak value of over 36 °C during the exercise activity. After t1, the skin tem- perature returns to baseline. Both the skin temperature and the rate of heat loss through the skin have similar curves, illustrating that a rising skin temperature goes hand in hand with a rising heat flux through the skin. Chart (d) shows the rate of change of the skin and core body temperature as determined using the skin and core body temperature, respectively. As shown, the rate of change is initially positive, before substantially leveling off, and finally, after t1, becoming negative as the skin and core body temperature declines and returns to baseline. Chart (e) shows the rate of change of thermal energy in the body, which is also positive during the first part of the exercise activity before stabilizing and finally, after t1, turning negative before returning to baseline, illustrating that the thermal energy stored in the body initially rises sharply in conjunction with the rise in skin temperature before stabiliz- ing and then returning to baseline after t1. Chart (f) shows the rate of energy expenditure of the person as calculated using a method as described herein, in particular equation 12. It can be seen that the rate of energy expenditure rises at t0 from a baseline value of approximately 100 W to above 1100 W during the exercise activity, remaining relatively stable during the exercise ac- tivity before falling sharply after t1 and returning to baseline. It is also evident that the rate of energy expenditure as calculated using the heat flux and the skin and core body temperature closely matches the metabolic power, shown in chart (a), determined using P28589PC00 26.05.2025 69 spirometry. Therefore, the methods of determining the rate of energy expenditure as described herein offer are a practicable alternative to using spirometry, in particular in situations where spirometry is not possible or would be too cumbersome to perform, such as during an outdoor activity. Fig.21 shows three charts (a – c) related to the energy expenditure of an exemplary person towards the end of an exercise activity and extending into the cool-down. The person has a weight of 70 kg, height of 180 cm, body surface area of approximately 1.85 square meters (according to the Du Bois and Du Bois formula), and an assumed specific heat capacity of 3.4 kJ / kg / K. All charts are time-series in minutes over the same time-span of 90 minutes. The first ten minutes are exercise, and the last 80 minutes are at rest. The time-point t0 is indi- cated and corresponds to the time-point at which the metabolic power generated by the person drops to baseline. The time-point t1 is indicated occurring approximately 40 minutes after t0 at which time-point the skin and core temperatures, as well as the heat flux through the skin, have returned substantially to baseline. The top chart (a) shows the metabolic power generated in the person’s body. The met- abolic power during exercise is at approximately 1200 W, while the baseline after ces- sation of exercise is at around 100 W. The increase in metabolic power during exercise is that which demands an increased rate of energy expenditure during exercise vs. rest. The kinetic power output by the athlete is subtracted from the metabolic power output, as the kinetic power output does not lead to an increase in the thermal energy in the body. As the kinetic efficiency of a human is around 25% for cycling, the majority of the energy consumed by the body during exercise does not result in kinetic power output but rather results in heating the body. P28589PC00 26.05.2025 70 The middle chart (b) shows the skin and core temperatures, respectively. It can be seen that the core temperature is at about 39 °C during the activity, the core cools down to a baseline of approximately 37 °C in the post-exercise time-period. The skin temperature is about 36 °C during exercise and drops down to a baseline of approximately 33 °C in the post-exercise time-period. The bottom chart (c) shows the heat flux as measured by a heat flux sensor worn in the chest area of the person. The heat flux as measured by the heat flux sensor is approxi- mately 600 W / m2 during exercise such that, when the heat flux is multiplied by the sur- face area of approximately 1.85 square meters, it is clear that the person has reached a quasi steady-state physiological condition in which the metabolic power is almost equal to the heat flowing out through the skin. The difference may be accounted for by, for example, respiratory heat loss, which may also be taken into account in the method 190 as an additional source of heat loss. The heat flux through the skin returns to a baseline value of approximately 41 W / m2. The heat flux correction term HFCT calculated using the energy expenditure data de- picted in Fig.20 has a value of 1.13. The above-described embodiments of the disclosure are exemplary and the person skilled in the art knows that at least some of the components and / or steps described in the embodiments above may be rearranged, omitted, or introduced into other embodi- ments without deviating from the scope of the present disclosure.

Claims

P28589PC00 26.05.2025 71 CLAIMS 1. A computer-implemented method for determining a rate of energy expenditure of a person, the method comprising: receiving (S13) a first measurement indicative of a rate of transfer of en- ergy from the body of a person to the environment; receiving (S13) a second measurement indicative of a measure of the thermal energy stored in the body of the person; calculating (S14) a change in the thermal energy stored in the body of the person using the second measurement; and calculating (S14) a rate of energy expenditure of the person using the rate of transfer of energy from the body of the person to the environment and the change in the thermal energy stored in the body.

2. The method according to claim 1, wherein receiving the first measurement indica- tive of a rate of transfer of energy from the body of the person to the environment comprises receiving a measurement of a flow of thermal energy from the body to the environment, in particular a measurement of a heat flux (HF) through the skin of the person.

3. The method according to one of claims 1 or 2, wherein receiving the second meas- urement indicative of a thermal energy stored in the body of the person comprises receiving a measured temperature of the body.

4. The method according to one of claims 2 or 3, wherein the method comprises:P28589PC00 26.05.2025 72 calculating a total heat flux (HF) through the skin of the person, using the heat flux (HF) and a pre-defined body surface area factor indicative of the total surface area of the person; and calculating (S15) the rate of energy expenditure of the person as a func- tion of the total heat flux through the skin and the change in the stored thermal energy in the person.

5. The method according to one of claims 1 to 4, wherein the method comprises: calculating (S14) the change in the thermal energy stored in the body of the person using a pre-defined heat capacity of the person and the second measurement.

6. The method according to one of the claims 1 to 5, wherein the method comprises calculating the rate of energy expenditure as a function which includes a sum of the heat flux through the skin and the change in the thermal energy stored in the body.

7. The method according to one of the claims 1 to 6, wherein the method comprises calculating the rate of change in the thermal energy stored in the body of the person using a heat capacity of the person, wherein the heat capacity of the person is determined using a pre-defined specific heat of a human body and a pre-defined mass of the person.

8. The method according to one of the claims 1 to 7, wherein the method comprises: calculating the rate of change in the thermal energy stored in the body of the person using a heat capacity of the person, wherein the heat capacityP28589PC00 26.05.2025 73 of the person is determined using a core heat capacity and a skin heat capacity, wherein: the measurement of a temperature of a person includes a core body temperature and a skin temperature, the core heat capacity is determined using a specific heat of the core of a human, a pre-defined mass of the core of the person, and a change in the core temperature, and the skin heat capacity is determined using a specific heat of the skin of a human, a pre-defined mass of the skin of the person, and a change in the skin temperature.

9. The method according to one of the claims 2 to 8, wherein the method comprises: calculating the heat flux through the skin using a pre-defined heat flux cor- rection term, wherein the heat flux correction term depends on a position on the body where the heat flux measurement is performed.

10. The method according to claim 9, wherein the pre-defined heat flux correction term is calculated using the change in the thermal energy stored in the body and the heat flux through the skin, in particular calculated as a function of the ratio of the change in the thermal energy to the heat flux through the skin.

11. The method according to any one of the claims 1 to 10, further comprising: receiving (133) a measurement of a kinetic power output of the person; andP28589PC00 26.05.2025 74 calculating (S134) the rate of energy expenditure of the person as a func- tion of the total heat flux through the skin, the rate of change of the stored body heat of the person and the kinetic power output of the person.

12. The method according to any one of the claims 1 to 11, further comprising: determining (S17) a cumulative energy expenditure using one or more values of the rate of energy expenditure determined during one or more pre-defined periods, respectively.

13. The method according to any one of the claims 1 to 12, further comprising: transmitting (S16, S18) a message indicative of a measure of energy ex- penditure, wherein the measure of energy expenditure comprises one or more of the following: the rate of energy expenditure or the cumulative energy expenditure.

14. The method according to any one of the claims 1 to 13, further comprising: calculating (S144) a rate of respiratory heat loss, the respiratory heat loss due to exhalation of warm water vapor, using the heat flux through the skin, the rate of change of the thermal energy stored in the body, and a respiratory heat loss factor; and calculating (S145) the energy expenditure of the person further using the respiratory heat loss.

15. The method according to one of the claims 1 to 14, wherein the method comprises:P28589PC00 26.05.2025 75 receiving a plurality of measurements of the heat flux (HF) through the skin and / or a plurality of measurements of the temperature, wherein at least some of the measurements are performed at different positions on the body of the person; calculating a single value for the heat flux (HF) using the plurality of meas- urements of the heat flux (HF); and calculating a single value for the temperature using the plurality of tem- perature measurements.

16. An electronic system (1) for determining a rate of energy expenditure of a person, the electronic system (1) comprising a processor (11) configured to perform the method according to one of claims 1 to 15.

17. The electronic system (1) according to claim 16, wherein the electronic system (1) further comprises: a wearable device (2) including a sensor system (3) configured to deter- mine the heat flux (HF) through the skin and a temperature of the person, wherein the sensor system (3) is worn on the body of the person.

18. The electronic system (1) according to claim 17, wherein the electronic system (1) comprises a plurality of wearable devices (2), each wearable device (2) including a sensor system (3), and the processor (11) is configured to receive data from the plurality of sensor systems (3) of the wearable devices (2).P28589PC00 26.05.2025 76 19. The electronic system (1) according to claim 17 or 18, wherein the sensor system (3) comprises a heat flux sensor (31) configured to determine heat flux (HF), wherein the heat flux sensor (31) is implemented using one or more of: a chip comprising a series of p- and n- doped semiconductors; or two stacked temperature sensors separated by a thermal resistance.

20. The electronic system (1) according to claim 16 to 19, further comprising one or more of the following sensors: a PPG sensor (34), an ECG sensor (35), a blood lactate sensor, a galvanic skin response sensor, a sweat rate sensor, one or more further skin temperature sensors, an ambient temperature sensor (33), or an ac- celerometer, and wherein the additional sensors are preferably integrated into the wearable device (2).

21. The electronic system (1) according to one of claims 17 to 20, wherein the proces- sor (11) is integrated into the wearable device (2).

22. The electronic system (1) according to one of claims 17 to 21, wherein the weara- ble device (2) includes a wireless communications module configured to generate and transmit a message indicative of a measure of energy expenditure, wherein the measure of energy expenditure comprises one or more of the following: the rate of energy expenditure or the cumulative energy expenditure.

23. The electronic system (1) according to one of claims 17 to 22, further comprising a separate electronic device (4, 6), the processor (11) integrated into the separate electronic device (4, 6); the wearable device (2) including a wireless communica- tions module configured to transmit a message including the heat flux (HF) and the temperature to the separate electronic device (4, 6).P28589PC00 26.05.2025 77 24. A computer program product for determining a rate of energy expenditure of a per- son, comprising computer program code configured to control a processor (11) such that the processor (11) performs the method according to one of claims 1 to 15.

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