Minimal Joint Entropy and Order-Preserving Couplings
Information Theory
2022-06-09 v1 math.IT
Probability
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.
Keywords
Cite
@article{arxiv.2206.03676,
title = {Minimal Joint Entropy and Order-Preserving Couplings},
author = {Ya-Jing Ma and Feng Wang and Xian-Yuan Wu and Kai-Yuan Cai},
journal= {arXiv preprint arXiv:2206.03676},
year = {2022}
}
Comments
10 pages