TITLE: Axioms for mutual information
QUESTION [8 upvotes]: I am interesting in axiomatic justifications for concepts in information theory. I have found many axiomatizations for Shannon's entropy and for the Kullback-Leibler divergence, as well as their variations (for some examples, see this survey or these books: 1, 2). However, I have not found any results directly for the mutual information.
Are there any results that show that some intuitive properties uniquely characterize the mutual information of a joint distribution of two random variables?

REPLY [3 votes]: My paper https://arxiv.org/pdf/2108.12647.pdf provides an answer to this question. In particular, here is a quote from the introduction:
Our main result is Theorem~6.6, where we prove that the mutual information $\mathbb{I}(\mathcal{X},\mathcal{Y})$ of an ordered pair of random variables is the unique function (up to an arbitrary multiplicative factor) on pairs of random variables satisfying the following axioms: