Minimal Joint Entropy and Order-Preserving Couplings

06/08/2022

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by   Ya-Jing Ma, et al.

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This paper focuses on the extreme-value problem for Shannon entropy of the joint distribution with given marginals. It is proved that the minimum-entropy coupling must be of order-preserving, while the maximum-entropy coupling coincides with the independent one. Note that in this sense, we interpret entropy as a measure of system disorder.