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|description=This paper is one of the few comprehensive introductory articles on the causal emergence theory and effective information (EI) in the integrated information theory in the current Internet world, including the source of effective information, the definition and decomposition of effective information, practical examples, and how to expand to continuous variables, what is the relationship with causal metrics and dynamic reversibility.

|description=This paper is one of the few comprehensive introductory articles on the causal emergence theory and effective information (EI) in the integrated information theory in the current Internet world, including the source of effective information, the definition and decomposition of effective information, practical examples, and how to expand to continuous variables, what is the relationship with causal metrics and dynamic reversibility.

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Effective Information (EI) is a core concept in the theory of [[Causal Emergence]], used to measure the strength of [[Causal Effects]] in [[Markov Dynamics]]. In this context, causal effect refers to the extent to which different input distributions lead to different output distributions when viewing the dynamics as a black box. The degree of this connection is the causal effect. EI can typically be decomposed into two components: Determinism and Degeneracy. Determinism indicates how well the next state of the system can be predicted from its previous state, while Degeneracy refers to how well one can infer the previous state from the next state. A system with higher Determinism or lower Degeneracy will have higher Effective Information. In this page, all [math]\log[/math] represent logarithmic operations with a base of 2.

Effective Information (EI) is a core concept in the theory of [[Causal Emergence]], used to measure the strength of [[Causal Effects]] in [[Markov Dynamics]]. In this context, causal effect refers to the extent to which different input distributions lead to different output distributions when viewing the dynamics as a black box, and the strength of this connection between the input and output distributions is the causal effect. EI can typically be decomposed into two components: Determinism and Degeneracy. Determinism indicates how well the next state of the system can be predicted from its previous state, while Degeneracy refers to how well one can infer the previous state from the next state. A system with higher Determinism or lower Degeneracy will have higher Effective Information. In this page, all [math]\log[/math] represent logarithmic operations with a base of 2.

=Historical Background=

=Historical Background=