Stochastic thermodynamics of a finite quantum system coupled to a heat bath

TL;DR

This paper develops a stochastic thermodynamics framework for finite quantum systems coupled to heat baths, deriving generalized Jarzynski-type equations and inequalities that describe heat and entropy flow without requiring thermalization.

Contribution

It introduces a general theoretical approach to analyze heat and entropy flow in finite quantum systems coupled to baths, extending existing thermodynamic relations.

Findings

Derived generalized Jarzynski-type equations for quantum systems.

Established inequalities relating entropy increase and heat transfer.

Provided an analytical example illustrating the theoretical results.

Abstract

We consider a situation where an $N$-level system (NLS) is coupled to a heat bath without being necessarily thermalized. For this situation we derive general Jarzinski-type equations and conclude that heat and entropy is flowing from the hot bath to the cold NLS and, vice versa, from the hot NLS to the cold bath. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities which have already been considered in the literature. Our approach is illustrated by an analytical example.