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Rosas et al. <ref name=":5" /> From the perspective of [[information decomposition]] theory, propose a method for defining causal emergence based on [[integrated information decomposition]], and further divide causal emergence into two parts: [[causal decoupling]] (Causal Decoupling) and [[downward causation]] (Downward Causation). Among them, causal decoupling represents the causal effect of the macroscopic state at the current moment on the macroscopic state at the next moment, and downward causation represents the causal effect of the macroscopic state at the previous moment on the microscopic state at the next moment. The schematic diagrams of causal decoupling and downward causation are shown in the following figure. The microscopic state input is <math>X_t\ (X_t^1,X_t^2,…,X_t^n ) </math>, and the macroscopic state is <math>V_t </math>, which is obtained by coarse-graining the microscopic state variable <math>X_t </math>, so it is a supervenient feature of <math>X_t </math>, <math>X_{t + 1} </math> and <math>V_{t + 1} </math> represent the microscopic and macroscopic states at the next moment respectively.

Rosas et al. <ref name=":5" /> From the perspective of [[information decomposition]] theory, propose a method for defining causal emergence based on [[integrated information decomposition]], and further divide causal emergence into two parts: [[causal decoupling]] (Causal Decoupling) and [[downward causation]] (Downward Causation). Among them, causal decoupling represents the causal effect of the macroscopic state at the current moment on the macroscopic state at the next moment, and downward causation represents the causal effect of the macroscopic state at the previous moment on the microscopic state at the next moment. The schematic diagrams of causal decoupling and downward causation are shown in the following figure. The microscopic state input is <math>X_t\ (X_t^1,X_t^2,…,X_t^n ) </math>, and the macroscopic state is <math>V_t </math>, which is obtained by coarse-graining the microscopic state variable <math>X_t </math>, so it is a supervenient feature of <math>X_t </math>, <math>X_{t + 1} </math> and <math>V_{t + 1} </math> represent the microscopic and macroscopic states at the next moment respectively.

[[文件:Causal_Emergence_Relationship_Diagram.png|替代=|无框|300x300像素]]

[[文件:Causal_Emergence_Relationship_Diagram.png|替代=|无框|400x300像素]]

=====Partial Information Decomposition=====

=====Partial Information Decomposition=====