Mutual information via thermodynamics: Three different approaches

TL;DR

This paper explores three thermodynamic methods to derive mutual information, involving modifications to the second law and energy definitions, and discusses a physical system realization and an information-heat engine.

Contribution

It introduces three novel thermodynamic approaches to quantify mutual information, extending traditional physics frameworks and proposing a physical information-heat engine.

Findings

Three thermodynamic approaches to mutual information derived

Extension of the second law required for these approaches

Proposal of a physical information-heat engine

Abstract

Three different approaches to derive mutual information via thermodynamics are presented where the temperature-dependent energy is given by: (a) $\beta \mathcal{E} = -\ln[P(X,Y)]$, (b) $\beta \mathcal{E} =-\ln[P(Y|X)]$ or (c) $\beta \mathcal{E} =-\ln[P(X|Y)]$. All approaches require the extension of the traditional physical framework and the modification of the 2nd law of thermodynamics. A realization of a physical system with an effective temperature-dependent Hamiltonian is discussed followed by a suggestion of a physical information-heat engine.