Identities for Entropy Change Associated with the Time-Evolution of an Open System

TL;DR

This paper derives general relations linking entropy change to the evolution of open quantum systems using real-time and imaginary-time formulations within quantum statistical mechanics, providing formulas for entropy production due to dissipation.

Contribution

It introduces new formulas connecting entropy change with system evolution and reservoir temperature variations in open quantum systems, based solely on standard quantum statistical mechanics.

Findings

Derived entropy change relations for open quantum systems

Obtained formulas for entropy production due to dissipation

Applied the theory to a model system demonstrating usefulness

Abstract

A general relation between entropy and an evolutionary superoperator is derived based on the theory of the real-time formulation. The formulation establishing the relation relies only on the framework of quantum statistical mechanics and the standard definition of the von Neumann entropy. Applying the theory of the imaginary-time formulation, a similar relation is obtained for the entropy change due to the change in reservoir temperatures. To show the usefulness of these formulas, we derived the expression for the entropy production induced by some dissipation in an open quantum system as the exemplary model system.