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Without loss of generality, assume that our microstate is <math>X(X^1,X^2)</math>, meaning it is a two-dimensional variable, and the macrostate is V. Then the [[mutual information]] between the two can be decomposed into four parts:

Without loss of generality, assume that our microstate is <math>X(X^1,X^2)</math>, meaning it is a two-dimensional variable, and the macrostate is V. Then the [[mutual information]] between them can be decomposed into four parts:

Among them, <math>Red(X^1,X^2;V)</math> represents [[redundant information]], which refers to the information repeatedly provided by two microstates <math>X^1</math> and <math>X^2</math> to the macrostate <math>V</math>; <math>Un(X^1;V│X^2)</math> and <math>Un(X^2;V│X^1)</math> represent [[unique information]], which refers to the information provided by each microstate variable alone to the macrostate; <math>Syn(X^1,X^2;V)</math> represents [[synergistic information]], which refers to the information provided by all microstates <math>X</math> jointly to the macrostate <math>V</math>.

Among them, <math>Red(X^1,X^2;V)</math> represents [[redundant information]], which refers to the information repeatedly provided by two microstates <math>X^1</math> and <math>X^2</math> to the macrostate <math>V</math>; <math>Un(X^1;V│X^2)</math> and <math>Un(X^2;V│X^1)</math> represent [[unique information]], which refers to the information provided by each microstate variable alone to the macrostate; <math>Syn(X^1,X^2;V)</math> represents [[synergistic information]], which refers to the information provided by all microstates <math>X</math> jointly to the macrostate <math>V</math>.

=====Definition of Causal Emergence=====

=====Definition of Causal Emergence=====