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===Minimum Value===

===Minimum Value===

From the first derivative of EI, we discussed the extreme value problem, showing that EI reaches a minimum of 0 when all the row vectors of the transition matrix are identical. Is this minimum value the lowest possible?

From the first derivative of EI, we discussed the extreme value problem, showing that EI reaches a minimum of 0 when all the row vectors of the transition matrix are identical. Is this minimum value the lowest possible value?

We know that based on Equation {{EquationNote|2}}, EI is essentially a form of KL divergence, which is always non-negative. Thus:

We know that based on Equation {{EquationNote|2}}, EI is essentially a form of KL divergence, which is always non-negative. Thus:

EI_{min}=0.

EI_{min}=0.

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===Maximum Value===

===Maximum Value===

From the previous discussion on determinism and degeneracy, we know that EI can be decomposed into two parts:

From the previous discussion on determinism and degeneracy, we know that EI can be decomposed into two parts: