Shannon Meets Carnot: Mutual Information Via Thermodynamics

TL;DR

This paper presents a novel thermodynamic framework for analyzing mutual information in Gaussian channels, linking information theory with fundamental physical laws and offering an alternative proof of a key theorem.

Contribution

It introduces a thermodynamic representation of Gaussian channels, connecting mutual information with thermodynamic quantities and generalizing the second law of thermodynamics.

Findings

Thermodynamic quantities can describe mutual information in Gaussian channels.

Provides an alternative proof of the Guo-Shamai-Verdú theorem.

Establishes a fundamental link between information theory and thermodynamics.

Abstract

In this contribution, the Gaussian channel is represented as an equivalent thermal system allowing to express its input-output mutual information in terms of thermodynamic quantities. This thermodynamic description of the mutual information is based upon a generalization of the $2^{nd}$ thermodynamic law and provides an alternative proof to the Guo-Shamai-Verd\'{u} theorem, giving an intriguing connection between this remarkable theorem and the most fundamental laws of nature - the laws of thermodynamics.