Statistical mechanical expression of entropy production for an open quantum system

TL;DR

This paper develops a quantum statistical framework for entropy production in open quantum systems, aligning microscopic dynamics with thermodynamic principles and providing a consistent way to compute entropy changes.

Contribution

It introduces a new quantum statistical expression for entropy that aligns with Gibbs' relation and relates system-reservoir interactions to entropy change operators.

Findings

Correct entropy production in linear response regime

Derivation based on microscopic time-evolution principles

Consistent with von Neumann entropy and Gibbs' relation

Abstract

A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs' relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in quantum mechanics. The general relation between system-reservoir interactions and an entropy change operator in an open quantum system, relying just on the framework of statistical mechanics and the definition of von Neumann entropy. By using this formula, we can obtain the correct entropy production in the linear response framework. The present derivation of entropy production is directly based on the first principle of microscopic time-evolution, while the previous standard argument is due to the thermodynamic energy balance.