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</math>

</math>

Here, [math]\alpha\in(0,2)[/math] is a specified parameter that acts as a weight or tendency to make [math]\Gamma_{\alpha}[/math] reflect determinism or degeneracy more. Under normal circumstances, we take [math]\alpha = 1[/math>, which can make [math]\Gamma_{\alpha}[/math> achieve a balance between determinism and degeneracy.

Here, [math]\alpha\in(0,2)[/math] is a specified parameter that acts as a weight or tendency to make [math]\Gamma_{\alpha}[/math] reflect determinism or degeneracy more. Under normal circumstances, we take [math]\alpha = 1[/math], which can make [math]\Gamma_{\alpha}[/math] achieve a balance between determinism and degeneracy.

In addition, the authors in the literature prove that there is an approximate relationship between <math>EI</math> and [math]\Gamma_{\alpha}[/math>:

In addition, the authors in the literature prove that there is an approximate relationship between <math>EI</math> and [math]\Gamma_{\alpha}[/math]:

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Moreover, to a certain extent, [math]\Gamma_{\alpha}[/math> can be used instead of EI to measure the degree of causal effect of Markov chains. Therefore, the so-called causal emergence can also be understood as an '''emergence of dynamical reversibility'''.

Moreover, to a certain extent, [math]\Gamma_{\alpha}[/math] can be used instead of EI to measure the degree of causal effect of Markov chains. Therefore, the so-called causal emergence can also be understood as an '''emergence of dynamical reversibility'''.

=====Quantification of Causal Emergence without Coarse-graining=====

=====Quantification of Causal Emergence without Coarse-graining=====