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Minimal Joint Entropy and Order-Preserving Couplings (2206.03676v1)
Published 8 Jun 2022 in cs.IT, math.IT, and math.PR
Abstract: 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.
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