Food safety risk assessment and early warning method based on network density matrix

Abstract

The invention discloses a method for carrying out modeling simulation analysis on regional pesticide residue diffusion by utilizing a network density matrix. The invention provides a novel food safety modeling theory by utilizing the latest progress of statistical physics and machine learning in the field of network flow. Entropy and free energy concepts in statistical physics are introduced, path diversity and signal speed in the network are quantitatively represented by constructing a network density matrix, and deep analysis is performed on an established dynamic weighted network model. According to the method, the diffusion path, speed and concentration change after pesticide residue leakage can be accurately simulated, and then the influence of pesticide residue leakage and diffusion on the region is analyzed. By providing a scientific quantitative analysis theory for food safety prediction, the risk supervision capability is effectively improved, and powerful support is provided for agricultural non-point source pollution treatment.

Description

Technical Field

[0001] The present invention relates to the field of food safety management, and specifically to a food safety risk assessment and early warning method based on a network density matrix. The method utilizes the latest advances in statistical physics and information dynamics to dynamically model and quantitatively analyze food safety risks such as pesticide residues. Background Art

[0002] Currently, most food safety research focuses on the end point of the "farm to table" process, with little research examining risk assessment and control at the source. Our research addresses this gap by focusing on "source control" to analyze the levels of pesticide residues in the soil and the impact of their spread on crops, conducting risk assessment and control, and ultimately ensuring food security.

[0003] Traditional food safety management methods rely heavily on static data analysis and empirical judgment, making them incapable of addressing complex and volatile food safety risks. This is particularly true for the spread of pesticide residues, where traditional fixed-point monitoring struggles to capture the dynamic diffusion patterns of pollutants. A spatially based early warning system is urgently needed. Complex network theory offers a new approach to addressing this challenge, but existing research still suffers from issues such as static topological analysis ignoring dynamic propagation characteristics and a lack of metrics for quantitatively evaluating critical pathways.

[0004] So far, there have been many classic network models for modeling complex networks, such as graph theory, ER network, WS small-world network, BA scale-free network, etc.

[0005] In the field of food safety, graph theory is mainly used to construct supply chain network topology models and analyze pollutant transmission paths and risk diffusion mechanisms, such as identifying key pollution sources or vulnerable transportation nodes through node centrality. The ER random network model can evaluate the probability of random contamination events in the food production process by simulating the random connection characteristics between nodes, providing a basic statistical framework for risk monitoring. The WS small-world network, due to its high clustering coefficient and short path characteristics, is used to optimize the efficiency of food recall information dissemination, for example, by adjusting the connection rules of supply chain nodes to accelerate the transmission of contamination warning signals. The BA scale-free network focuses on identifying hub nodes in the food supply chain, such as large distribution centers. Its preferential connection mechanism can quantify the impact of key node failure on the stability of the global network, providing a topological structure-level decision-making basis for risk prevention and control.

[0006] In recent years, my country has faced severe challenges in food safety, with pollution at the source being a particular concern. Complex network theory offers a new approach to addressing this challenge. This theory integrates multi-source data through a node-edge structure, abstracting geographic units into network topologies. While its effectiveness has been demonstrated in areas such as pollutant diffusion, it still faces shortcomings: first, static topological analysis ignores dynamic propagation characteristics; second, there is a lack of an indicator system for quantitatively evaluating critical pathways.

[0007] Therefore, there is an urgent need to find a dynamic weighted network model to break through the limitations of traditional research, characterize the network structure and dynamic process at the same time, and describe the problem of the spread of pesticide residues from pollution sources among farmlands. Summary of the Invention

[0008] In response to the above problems, in order to further analyze the problem of pesticide residue diffusion at the source of agricultural product pollution, the present invention proposes a breakthrough using the information dynamics method in statistical physics. Its density matrix, partition function and other tools can simultaneously characterize the network structure and dynamic process. The network entropy and free energy indicators correspond to the diversity and efficiency of the transmission path, respectively, which are highly consistent with the migration characteristics of pesticide residues.

[0009] This invention innovatively constructs a dynamic weighted network model, breaking through the limitations of traditional research. It applies the concept of density matrices in quantum statistical physics to network density matrices, thereby dynamically modeling pesticide diffusion. Furthermore, the invention utilizes the concepts of information entropy and free energy to analyze dynamic network characteristics and quantify the characteristics of pesticide diffusion within the network. This invention provides a new tool for the management of agricultural non-point source pollution, supports the formulation of differentiated management and control strategies, and is expected to have significant application value in areas such as ecological restoration.

[0010] Compared with the traditional method, the beneficial effects of the method of the present invention are:

[0011] ① This invention is the first to extend the concept of density matrix in statistical physics to network density matrix, and combines it with Laplace matrix to construct a dynamic weighted network model to dynamically simulate the diffusion process of pesticide residues in complex ecosystems.

[0012] ② The present invention uses two macroscopic physical indicators, information entropy and free energy of the von Neumann network, to quantify the path diversity and pesticide propagation speed of pesticide diffusion in the network, providing a new quantitative tool for accurately evaluating the diffusion characteristics of pesticides.

[0013] ③ Unlike traditional research that focuses on the end of food safety, this invention is oriented towards "source" control. By analyzing the content of pesticide residues in the soil and the impact on crops during transmission, it fills the gap in food safety source risk warning and provides a more comprehensive perspective for food safety risk management. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a flowchart of the present invention using network density matrix to model the diffusion of pesticide residues, and using network information entropy and free energy to analyze the network to achieve the purpose of risk warning.

[0015] Figure 2 This is a comparison diagram of the actual geographical map of Changping District, Beijing, and the modeled network topology according to an embodiment of the present invention.

[0016] Figure 3 This is a simulation result diagram of pollution levels of time-series pesticide residue diffusion according to an embodiment of the present invention.

[0017] Figure 4 A visual adjacency matrix diagram of the model built in an embodiment of the present invention.

[0018] Figure 5 This is a visualization simulation result diagram of the information entropy and free energy of the model network built in an embodiment of the present invention. DETAILED DESCRIPTION

[0019] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0020] The present invention proposes a method for modeling and analyzing the diffusion of pesticide residues using a network density matrix. The method is described in two parts. The first part is how to construct a network model for the diffusion of pesticide residues and analyze the network by calculating the von Neumann network information entropy and free energy. The second part is to apply the pesticide residue diffusion network model constructed by the present invention, and to perform risk management of the network by calculating the obtained von Neumann network information entropy and free energy, so as to achieve the purpose of food safety risk early warning.

[0021] Part I: Building a network model for pesticide residue diffusion

[0022] In the present invention, Figure 1 This is a flowchart of the entire process of building a pesticide residue diffusion network model. Specifically, the steps of building a pesticide residue diffusion network model using the network density matrix method are:

[0023] Construction step A, normalizing geographic map data;

[0024] In the present invention, the farmland network model is constructed based on a public geographic map.

[0025] In the present invention, the geographic map data at least includes: farmland location data and data on the distance between farmlands, etc., which provides a basis for the spatial analysis of the model.

[0026] In the present invention, based on these public geographic spatial data and combined with statistical physics and network density matrix modeling methods, an in-depth analysis and prediction of the pesticide residue diffusion situation in the actual farmland is carried out.

[0027] Construction step B, constructing the Laplace matrix;

[0028] For example, a network model is established by using the standardized actual geographic map data obtained in step A, thereby establishing an adjacency matrix A (Adjacency Matrix) based on the actual geographic map.

[0029] In the present invention, the adjacency matrix A used is a mathematical tool used in network science to describe the connection relationship between nodes. The connection is usually encoded by the adjacency matrix A, where if nodes i and j are connected, then A ij =1, otherwise A ij = 0. For weighted networks, the value A ij It can be non-binary. The information exchange between components is carried out through connections, which is one of the simplest and most common ways to spread attention. The degree matrix D (diagonal matrix) is a diagonal matrix. ii =k i Represents the connectivity of node i, which indicates the number of edges directly connected to the node. From this, the Laplacian matrix L (Laplacian matrix) is constructed to control the information flow. The Laplacian matrix formula is:

[0030] L=DA (1)

[0031] Construction step C, constructing a dynamic weighted network model using a network density matrix based on a Laplace matrix;

[0032] In this invention, farmland in the actual geographical map is selected as the network node, and the connection between nodes is established according to the principle of spatial proximity to form a complex network. The Laplace matrix is ​​introduced to integrate the connectivity and degradation rate, and a dynamic weighted network model is constructed to more accurately simulate the diffusion process of pesticides in the complex network. The diffusion equation can be obtained from step B. and its solution ψ τ =e -τL ψ0. Among them, ψ τ is a concentration vector that describes the distribution of a quantity at a node. -τL is represented as a time evolution operator, and e -τL ] ij It is expressed as the flow from node i to node j after time step τ. Thus, the concept of density matrix in statistical physics is extended to the field of complex networks. The network density matrix is ​​a mathematical tool used to describe the information dynamics on complex networks. The network density matrix can be generalized as shown in formula (2).

[0033]

[0034] τ is the propagation scale.

[0035] e -τL It is represented as a time evolution operator.

[0036] Tr(e -τL ) is the network counterpart of the partition function, called the network partition function Z τ , used to derive macroscopic statistical properties in computational networks.

[0037] The network density matrix is ​​both a modeling method used to construct and describe information flow models within a network and a network measurement tool, assessing the network's information flow performance through derived macroscopic physical quantities. It plays a key role in the analysis of complex networks and the understanding of dynamic processes. As a tool combining modeling and measurement capabilities, the network density matrix plays an important role in complex network research, providing strong mathematical support for understanding network information flow, optimizing network structure, and achieving network compression.

[0038] The standardized geographic data map obtained in step A is combined with the network density matrix obtained in step C to establish a network model of farmland points based on the actual geographic map.

[0039] Construction step D: constructing a complex network model of pesticide residue diffusion;

[0040] In the present invention, the diffusion of pesticide residues in the farmland network is simulated based on the concentration diffusion and network density matrix formula (2) in step C. The network density matrix can capture the statistical correlation and dynamic behavior of network nodes, providing a mathematical tool for quantitatively evaluating pesticide diffusion characteristics and analyzing the impact of pesticide leakage events on each farmland.

[0041] In the present invention, each farmland in the actual geographical map is regarded as a node, and the connection relationship between each farmland is regarded as the connectivity of the network node. When the distance between two farmlands is less than the transmission distance of pesticide residues, the two farmland network nodes can be regarded as connected to each other. Then, the pesticide diffusion is simulated according to the network density matrix to form a complex network model of pesticide residue diffusion.

[0042] Construct step E, using thermodynamic concepts to analyze complex network characteristics;

[0043] In this invention, the concepts of entropy and free energy in thermodynamics are extended to the field of complex networks to analyze the characteristics of the network model established in step D. Just like equilibrium thermodynamics, macroscopic thermodynamic physical indicators such as von Neumann entropy (network information entropy) and free energy are used to measure the macroscopic characteristics of the network system.

[0044] Among them, the network counterpart of the partition function is called the network partition function, and the formula is:

[0045] <![CDATA[Z τ =Tr(e -τL )]]> (3)

[0046] τ is the propagation scale.

[0047] e -τL It is represented as a time evolution operator.

[0048] L is the Laplace matrix.

[0049] In the present invention, the thermodynamic macroscopic indicators for analyzing the network characteristics in a complex network are mainly divided into three types: free energy, internal free energy and network information entropy.

[0050] In the present invention, the network density matrix formula (2) and related research can be used to define the free energy of the network as a measure of the system's signal propagation speed in the network. The positive or negative value of the free energy reflects the difficulty of information flow or material transmission in the system. When the free energy takes a non-zero value, it means that the system is in a non-equilibrium state, while when the free energy takes a zero value, it means that the system is in equilibrium or dynamic equilibrium.

[0051] The formula for calculating free energy is:

[0052]

[0053] τ is the propagation scale.

[0054] Z τ is the network partition function.

[0055] In the present invention, the free energy formula (4) is used to quantify the diffusion speed of pesticides in the network.

[0056] According to the network density matrix formula (2) and related research, the internal free energy of the network, that is, the internal energy, can be defined as:

[0057]

[0058] τ is the propagation scale.

[0059] Z τ is the network partition function.

[0060] In the present invention, the internal energy of a complex network can be calculated using formula (5). Internal energy focuses on describing the interactions between nodes within the network and the impact of these interactions on signal transmission speed. However, in the present invention, internal energy is mainly used as an intermediate variable when calculating entropy.

[0061] Based on the network density matrix formula (2) and related research, the information entropy of the network can be defined as a measure of the diversity of the system disturbance response in the network.

[0062] The formula for calculating entropy is:

[0063] <![CDATA[S τ =τ(U τ -F τ )]]> (6)

[0064] τ is the propagation scale.

[0065] U τ is the internal energy in the network.

[0066] F τ is the free energy in the network.

[0067] In the present invention, formula (6) is used to quantify the diversity of diffusion paths of pesticide residues in the network.

[0068] In the present invention, free energy reflects the speed of pesticide diffusion. The lower its value, the smoother and faster the diffusion process. Information entropy is used to describe the diversity of pesticide diffusion. The higher its value, the greater the diversity of pesticide distribution among different paths.

[0069] Construct step F to conduct risk assessment and early warning analysis on complex networks;

[0070] In this paper, the diversity and efficiency of pesticide diffusion pathways are assessed based on the quantification of information entropy and free energy. Key pollution sources and diffusion pathways are identified, providing a scientific basis for developing risk warning and control strategies.

[0071] Part II: Application of network density matrix to establish pesticide residue diffusion network model and analyze and realize food safety risk early warning

[0072] Application Objects

[0073] In the embodiment of the present invention, the research object modeled according to the actual geographical map is Changping District, Beijing. The farmland points in Changping District, Beijing are analyzed after network modeling.

[0074] like Figure 1 As shown, the basic idea of ​​implementing this embodiment is:

[0075] Firstly, based on data processing of actual geographic maps, the obtained geographic map data are normalized to obtain standardized data.

[0076] Secondly, the standardized data was used to build a model, and a model for pesticide diffusion prediction was established through the network density matrix.

[0077] Third, the established model was analyzed by calculating the network information entropy and free energy to quantify the pesticide diffusion speed and the diversity of pesticide diffusion paths, respectively, to analyze the network.

[0078] Finally, risk warning is carried out through calculation and analysis of the established model, and the results obtained from the analysis network are used to quantify the line warning, thus obtaining a complete time-series pesticide diffusion risk warning model.

[0079] A network density matrix was used to establish a pesticide residue diffusion network model in Changping District, Beijing, and the network was analyzed to achieve food safety risk early warning. The following steps were involved:

[0080] Step 1: Build a farmland network model in Changping District, Beijing;

[0081] Step 101: Modeling is performed based on the actual geographical map of Changping District, Beijing; an ERBG graph is used to construct an energy transfer bond graph belonging to the Gulfstream G650 aircraft;

[0082] Step 102, initializing the network model;

[0083] The network modeling is carried out based on the actual geographical map of Changping District, Beijing, which includes the location of farmland points and the distance between farmlands. Figure 2 As shown in the figure, it is a comparison diagram between the actual geographical map and the network topology of the established model. The left picture is the actual map of Changping District, Beijing, and the right picture is the network topology map after modeling.

[0084] The initial pesticide residue values ​​for each node in the model were set to 0. A random farmland location within the modeling area experienced a large pesticide spill. This allowed for a more intuitive observation of the impact of the spill on other farmland nodes in the network. The model also allowed for analysis of the impact of the spill on surrounding farmland. Sudden incidents warrant significant attention, as pesticide spills pose significant potential risks to the environment and farmland.

[0085] Step 2: simulate the diffusion of pesticide residues in the network;

[0086] The model established based on the actual geographical map of Changping District, Beijing is combined with formula (1) to construct the Laplace matrix of the model established based on the actual geographical map of Changping District, Beijing.

[0087] The network model of the embodiment is constructed by combining the Laplace matrix constructed based on the actual geographical map of Changping District, Beijing, with the network density matrix of formula (2). The network density matrix is ​​used to simulate the diffusion of pesticide residues in the network.

[0088] like Figure 3As shown in the figure, the diffusion of pesticide residues in the network of the embodiment forms a pollution level map. The color depth in the pollution level simulation experiment results map represents the degree of pesticide residue contamination in the farmland nodes. The established sophisticated model can simulate the diffusion path, speed, and concentration changes after pesticide leakage. Figure 3 The data showed that after the leak, the pesticide quickly spread to the surrounding farmland. Farmland in different locations was contaminated to varying degrees, demonstrating the significant impact of pesticide leaks on the farmland environment.

[0089] The modeling diffusion result diagram of the embodiment depicts the changes in the diffusion process of the pesticide in the network structure in detail through four time periods. Figure 3 It can be observed that the scope of influence of pesticides gradually expands over time. At the initial moment when the pesticides are just leaked, only the leaking node is affected, which appears dark red, and the rest of the nodes are light yellow. After a period of diffusion, the scope of influence has expanded significantly, and the colors of some nodes have deepened, indicating that the pesticides are spreading in the network and the pesticide concentrations at each node have increased. After a period of time, more nodes are dyed dark red and dark orange, showing that the pesticides have further spread and the concentrations have reached higher values ​​in some areas. Finally, at the final moment of the simulation, although the colors of some nodes have weakened, the scope of influence of pesticides is basically stable overall, and the dark red and dark orange nodes are widely distributed, indicating that the diffusion of pesticides in the network is now tending to balance. From the third stage to the fourth stage, the distribution of pesticides has not changed much, which indicates that the diffusion of pesticides may have been basically completed in the third stage and the diffusion of pesticides has tended to stabilize. It can be clearly seen from the color gradient bar that the color gradually changes from yellow to red, indicating that the pesticide concentration is from low to high. This result helps to understand the diffusion dynamics of pesticides in the network structure and provide data support for predictions and interventions in similar situations.

[0090] Step 3: Analysis of simulation network results;

[0091] By conducting network modeling on the actual geographical map of Changping District, Beijing, the adjacency matrix of the established network model is visualized, as shown in the figure below: Figure 4 shown.

[0092] Adjacency matrix is ​​a core tool in network science. We use a black and white grid structure to visually present the underlying network topology on which pesticide diffusion depends, such as Figure 4As shown. It can be seen from the figure that the visualized adjacency matrix is ​​a diagonal matrix, which further proves that the established model is correct, reliable and consistent with the basic theory. Each black square in the matrix represents a direct connection between two nodes. This connection may be a relationship or channel between adjacent farmland paths in physical space. For example, when the intersection of a farmland node and another farmland node is black, it indicates that pesticides may migrate between the two farmlands through the path. The diagonal of the matrix usually remains blank because there is no diffusion path between the node and itself. This design allows effective connections in the network to be quickly identified. It is worth noting that the distribution density and aggregation pattern of the black squares in the matrix have important implications - dense black areas may correspond to core areas where agricultural activities are concentrated. Such node groups become hotspots for pesticide diffusion due to their high degree of interconnection. This structural feature provides a spatial basis for subsequent analysis of the diversity of pesticide diffusion paths.

[0093] The network system characteristics of the established model are analyzed and evaluated by calculating two thermodynamic indicators: free energy in the network and von Neumann network information entropy.

[0094] By combining formula (3) with formula (4), the free energy is calculated, and the free energy in the network at each moment is calculated and recorded in real time. By combining formula (3), formula (5) and formula (6), the information entropy in the network is calculated, and the information entropy in the network at each moment is also calculated and recorded in real time. The network free energy and information entropy at each moment obtained by calculation are observed and analyzed, as shown in Figure 2. Figure 5 As shown, these are the free energy and information entropy in the network calculated at each moment.

[0095] Information entropy is used here to describe the diversity of pesticide diffusion processes; higher values ​​indicate greater diversity in the distribution of pesticides across different pathways. Free energy reflects the speed of pesticide diffusion; lower values ​​indicate a smoother and faster diffusion process.

[0096] Depend on Figure 5 As shown, as the system develops, information entropy gradually increases, indicating that the system's disorder is increasing and the pesticide diffusion paths are becoming more diverse. At the same time, free energy gradually decreases, indicating that the system's energy state is decreasing, which means that the diffusion rate of pesticides in the network is accelerating. These two thermodynamic indicators provide us with a powerful tool to deeply understand the dynamics of pesticide diffusion in network systems.

[0097] Among them, the free energy is negative and gradually approaches 0 over time. The free energy is negative and gradually approaches 0. This indicates that the system is in the transition stage from non-equilibrium to equilibrium. At this time, the system still has the driving force for spontaneous reaction, but the driving force gradually weakens and eventually reaches dynamic equilibrium. From the experimental results Figure 3As can be observed, the free energy in this network is negative. In network science, free energy measures the speed of signal transmission between nodes, and its positive or negative value reflects the ease of information flow or material transport within the system. A negative value indicates that the pesticide diffusion process in the network proceeds smoothly and rapidly, indicating that efficient transmission pathways exist in the system, allowing the pesticide to quickly diffuse from areas of high concentration to areas of low concentration. This reflects the facilitation of pesticide diffusion by the network structure. A negative free energy approaching zero corresponds to a steady-state state of pollutant diffusion, such as when the concentration gradient disappears.

[0098] The value of the adjacency matrix in the experimental result graph lies not only in the visualization of static structure, but also in its synergistic interpretation with dynamic indicators such as information entropy and free energy. Figure 3 Pollution level map and Figure 4 When comparing the adjacency matrix, we can see that highly connected nodes tend to appear darker, indicating a positive correlation between network connectivity and pollution accumulation. For example, if a pesticide spill occurs at a farm node, if that farm node is connected to multiple other farm nodes in the matrix, it could potentially continue to spread pesticide runoff to other farms, further spreading the residue and contaminating the environment and crops. Furthermore, if spills occur at farm nodes surrounding that farm node, highly connected nodes are more susceptible to the impact than other nodes. In reality, they could become pollution sinks by continuously receiving pesticide runoff from other farms. This correlation reveals the decisive role of network topology in the spatial distribution of pollutants: highly connected nodes are both the starting point for diffusion and the destination for pollution accumulation.

[0099] From the perspective of practical application, the experimental results provide dual inspiration for pollution prevention and control. The key hub nodes revealed by the adjacency matrix, such as the "bridge" nodes connecting multiple subnetworks, suggest that the core diffusion path can be blocked through targeted intervention, such as establishing buffer zones at the junction of farmlands, or converting hub farmlands with high pollution risks to adsorption crops. The low-connectivity areas identified in the matrix may represent ecologically fragile areas. Although these areas are not seriously polluted for the time being, they are at risk of sudden pollution due to the single connection path, and monitoring and early warning need to be strengthened. More in-depth analysis, combining the topological characteristics of the adjacency matrix with the free energy change curve, can quantitatively evaluate the effectiveness of different governance strategies - if the free energy decreases slowly after cutting off a key connection, it proves that the intervention has effectively delayed the diffusion process.

Claims

1. A method for conducting risk warning analysis on food safety by constructing a complex network model of pesticide residue diffusion through complex networks to simulate the spread of pesticide residue pollution in the environment, characterized by Constructing a complex network model of pesticide residue diffusion includes the following steps: Construction step A, normalizing geographic map data; The required geographic map data is normalized to obtain standardized data, including the location of each farmland point and the distance between farmland nodes and other actual data, in preparation for subsequent modeling and research. Construction step B, constructing the Laplace matrix; The adjacency matrix A is a mathematical tool used in network science to describe the connection relationship between nodes. Connections are usually encoded by the adjacency matrix A, where if nodes i and j are connected, then A ij =1, otherwise A ij = 0. For weighted networks, the value A ij Can be non-binary. Information exchange between components is carried out through connections, which is one of the simplest and most common ways to spread attention. The degree matrix D is a diagonal matrix, D ii =k i Represents the connectivity of node i, which indicates the number of edges directly connected to the node. From this, the Laplace matrix is ​​constructed to control the information flow. The Laplace matrix is ​​defined as: Construction step C, constructing a dynamic weighted network model using a network density matrix based on a Laplace matrix; Select farmland as network nodes, establish connections between nodes based on the principle of spatial proximity, and form a complex network. Introduce the Laplace matrix to integrate connectivity and degradation rate, and construct a dynamic weighted network model to more accurately simulate the diffusion process of pesticides in complex networks. The diffusion equation can be obtained from step B and its solution ψ τ =e -τL ψ0. Among them, ψ τ is a concentration vector that describes the distribution of a quantity at a node. -τL is represented as a time evolution operator, and e -τL ] ij It is expressed as the flow from node i to node j after time step τ. Thus, the concept of density matrix in statistical physics is extended to the field of complex networks. The network density matrix is ​​a mathematical tool used to describe the information dynamics on complex networks. The network density matrix can be generalized as shown in formula (2). τ is the propagation scale. e -τL It is represented as a time evolution operator. Tr(e -τL ) is the network counterpart of the partition function, called the network partition function Z τ , used to derive macroscopic statistical properties in computational networks. The network density matrix is ​​both a modeling method used to construct and describe information flow models within a network and a network measurement tool, assessing the network's information flow performance through derived macroscopic physical quantities. It plays a key role in the analysis of complex networks and the understanding of dynamic processes. As a tool combining modeling and measurement capabilities, the network density matrix plays an important role in complex network research, providing powerful mathematical support for understanding network information flow, optimizing network structure, and achieving network compression. The standardized geographic data map obtained in step A is combined with the network density matrix obtained in step C to establish a network model of farmland points based on the actual geographic map. Construction step D: constructing a complex network model of pesticide residue diffusion; The diffusion of pesticide residues in the farmland network is simulated according to the concentration diffusion and network density matrix formula (2) in step C. The network density matrix can capture the statistical correlation and dynamic behavior of network nodes, providing a mathematical tool for quantitatively evaluating the diffusion characteristics of pesticides and analyzing the impact of pesticide leakage events on each farmland. Construct step E, using thermodynamic concepts to analyze complex network characteristics; Applying concepts such as entropy and freedom from thermodynamics and extending them to the field of complex networks, we analyze the characteristics of the network model established in Step D. Similar to equilibrium thermodynamics, macroscopic thermodynamic physical indicators such as the network's von Neumann entropy and free energy are used to measure the macroscopic characteristics of the network system. Free energy reflects the rate of pesticide diffusion; lower values ​​indicate smoother and faster diffusion. Information entropy, on the other hand, describes the diversity of pesticide diffusion; higher values ​​indicate greater diversity in the distribution of pesticides across different pathways. Among them, the network counterpart of the partition function is called the network partition function, and the formula is: τ is the propagation scale. e -τL It is represented as a time evolution operator. L is the Laplace matrix. Construct step F to conduct risk assessment and early warning analysis on complex networks; Based on the quantitative results of information entropy and free energy, the diversity and efficiency of pesticide diffusion pathways are evaluated. Key pollution sources and diffusion pathways are identified, providing a scientific basis for formulating risk warning and control strategies.

2. The method of using a network density matrix to model a complex network of farmland points and using relevant concepts in equilibrium thermodynamics to analyze the complex network according to claim 1, to study the characteristics of pesticide residue diffusion in the complex network, characterized in that The macroscopic physical indicators in construction step E include: Thermodynamic macroscopic indicators for analyzing network characteristics in complex networks are mainly divided into three types: free energy, internal free energy and network entropy. Based on the network density matrix formula (2) and related research, the free energy of the network can be defined as a measure of the speed at which signals propagate in the network. The positive or negative value of the free energy reflects the difficulty of information flow or material transmission in the system. When the free energy takes a non-zero value, it means that the system is in a non-equilibrium state, while when the free energy takes a zero value, it means that the system is in equilibrium or dynamic equilibrium. The formula for calculating free energy is: τ is the propagation scale. Z τ is the network partition function. In the present invention, the free energy formula (4) is used to quantify the diffusion speed of pesticides in the network. According to the network density matrix formula (2) and related research, the internal free energy of the network, that is, the internal energy, can be defined as: τ is the propagation scale. Z τ is the network partition function. In the present invention, the internal energy of a complex network can be calculated using formula (5). Internal energy focuses on describing the interactions between nodes within the network and the impact of these interactions on signal transmission speed. However, in the present invention, internal energy is mainly used as an intermediate variable when calculating entropy. Based on the network density matrix formula (2) and related research, the information entropy of the network can be defined as a measure of the diversity of the system disturbance response in the network. The formula for calculating entropy is: τ is the propagation scale. U τ is the internal energy in the network. F τ is the free energy in the network. In the present invention, formula (6) is used to quantify the diversity of diffusion paths of pesticide residues in the network. In the present invention, free energy reflects the speed of pesticide diffusion. The lower its value, the smoother and faster the diffusion process. Information entropy is used to describe the diversity of pesticide diffusion. The higher its value, the greater the diversity of pesticide distribution among different paths.

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