Shannon Meets Carnot: Mutual Information Via 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.