Theory of Entropy Production in Quantum Many-Body Systems

TL;DR

This paper develops a quantum theoretical framework for entropy production in many-body systems, defining an entropy operator and deriving thermodynamic laws, with applications to classical and quantum transport phenomena.

Contribution

It introduces a quantum entropy operator, provides a method to extract its measurable part, and derives thermodynamic laws within a quantum many-body context.

Findings

Derived thermodynamic laws for isolated quantum systems.

Expressed entropy production and transport in weakly-coupled subsystems.

Validated the framework with classical and quantum transport examples.

Abstract

We define the entropy operator as the negative of the logarithm of the density matrix, give a prescription for extracting its thermodynamically measurable part, and discuss its dynamics. For an isolated system we derive the first, second and third laws of thermodynamics. For weakly-coupled subsystems of an isolated system, an expression for the long time limit of the expectation value of the rate of change of the thermodynamically measurable part of the entropy operator is derived and interpreted in terms of entropy production and entropy transport terms. The interpretation is justified by comparison to the known expression for the entropy production in an aged classical Markovian system with Gaussian fluctuations and by a calculation of the current-induced entropy production in a conductor with electron-phonon scattering.