A new approach to mutual information. II

TL;DR

This paper introduces a novel concept called mutual pressure for potential functions on various spaces, exploring its relationship with pressure and mutual information, extending previous work by Hiai and Petz.

Contribution

It presents a new approach to mutual information using mutual pressure and connects it with existing concepts, advancing theoretical understanding.

Findings

Mutual pressure relates to traditional pressure and mutual information.

The concept applies to both continuous and discrete spaces.

Extends prior work by Hiai and Petz.

Abstract

A new concept of mutual pressure is introduced for potential functions on both continuous and discrete compound spaces via discrete micro-states of permutations, and its relations with the usual pressure and the mutual information are established. This paper is a continuation of the paper of Hiai and Petz in Banach Center Publications, Vol. 78.