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In discrete-state systems, when comparing systems of different scales, we can compute either the direct EI difference or the normalized EI difference. Normalized EI is divided by [math]\log N[/math], where [math]N=\#(\mathcal{X})[/math] represents the number of elements in the discrete state space [math]\mathcal{X}[/math].

In discrete-state systems, when comparing systems of different scales, we can compute either the direct EI difference or the normalized EI difference. Normalized EI is divided by [math]\log N[/math], where [math]N=\#(\mathcal{X})[/math] represents the number of elements in the discrete state space [math]\mathcal{X}[/math].

However, for continuous variables, if the original EI is used, an unreasonable result may occur. Firstly, as shown in equation {{EquationNote|6}}, the EI formula contains a term [math]\ln L^n[/math]. Since L is a large positive number, the EI result will be significantly affected by L. Secondly, when calculating normalized EI (Eff), the issue arises that for continuous variables, the number of elements in the state space is infinite. A potential solution is to treat the volume of the space as the number N, and thus normalize it by [math]n \ln L[/math], meaning it is proportional to n and ln L:

However, for continuous variables, if the original EI is used, an unreasonable result may occur. Firstly, as shown in equation {{EquationNote|6}}, the EI formula contains a term [math]\ln L^n[/math]. Since L is a large positive number, EI will be significantly affected by L. Secondly, when calculating normalized EI (Eff), the issue arises that for continuous variables, the number of elements in the state space is infinite. A potential solution is to treat the volume of the space as the number N, and thus normalize it by [math]n \ln L[/math], meaning it is proportional to n and ln L:

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