Shannon Meets Carnot: Generalized Second Thermodynamic Law

TL;DR

This paper generalizes the second thermodynamic law to systems with temperature-dependent energy levels, linking thermodynamics with information theory and revealing new insights into the fundamental nature of temperature and mutual information.

Contribution

It introduces a generalized second law for systems with temperature-dependent Hamiltonians, connecting thermodynamics with information processing systems.

Findings

Generalized second law for temperature-dependent systems

New definition of temperature in thermodynamics

Expressed mutual information as a thermodynamic consequence

Abstract

The classical thermodynamic laws fail to capture the behavior of systems with energy Hamiltonian which is an explicit function of the temperature. Such Hamiltonian arises, for example, in modeling information processing systems, like communication channels, as thermal systems. Here we generalize the second thermodynamic law to encompass systems with temperature-dependent energy levels, $dQ=TdS+<d\mathcal{E}/dT>dT$, where $<\cdot>$ denotes averaging over the Boltzmann distribution and reveal a new definition to the basic notion of temperature. This generalization enables to express, for instance, the mutual information of the Gaussian channel as a consequence of the fundamental laws of nature - the laws of thermodynamics.