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[[文件:Gamma例子.png|居左|500x500像素|<math>EI</math>与<math>\Gamma</math>对比]]

[[文件:Gamma例子.png|居左|500x500像素|<math>EI</math>与<math>\Gamma</math>对比]]

The author gives four specific examples of Markov chains. The state transition matrix of this Markov chain is shown in the figure. We can compare the <math>EI</math> and approximate dynamical reversibility (the <math>\Gamma</math> in the figure, that is, <math>\Gamma_{\alpha = 1}</math>) of this Markov chain. Comparing figures a and b, we find that for different state transition matrices, when <math>EI</math> decreases, <math>\Gamma</math> also decreases simultaneously. Further, figures c and d are comparisons of the effects before and after coarse-graining. Among them, figure d is the coarse-graining of the state transition matrix of figure c (merging the first three states into a macroscopic state). Since the macroscopic state transition matrix in figure d is a deterministic system, the normalized <math>EI</math>, <math>eff\equiv EI/\log N</math> and the normalized [math]\Gamma[/math>: <math>\gamma\equiv \Gamma/N</math> all reach the maximum value of 1.

The author gives four specific examples of Markov chains. The state transition matrix of this Markov chain is shown in the figure. We can compare the <math>EI</math> and approximate dynamical reversibility (the <math>\Gamma</math> in the figure, that is, <math>\Gamma_{\alpha = 1}</math>) of this Markov chain. Comparing figures a and b, we find that for different state transition matrices, when <math>EI</math> decreases, <math>\Gamma</math> also decreases simultaneously. Further, figures c and d are comparisons of the effects before and after coarse-graining. Among them, figure d is the coarse-graining of the state transition matrix of figure c (merging the first three states into a macroscopic state). Since the macroscopic state transition matrix in figure d is a deterministic system, the normalized <math>EI</math>, <math>eff\equiv EI/\log N</math> and the normalized [math]\Gamma[/math]: <math>\gamma\equiv \Gamma/N</math> all reach the maximum value of 1.