Extended Clausius Relation and Entropy for Nonequilibrium Steady States in Heat Conducting Quantum Systems

TL;DR

This paper derives a quantum version of the extended Clausius relation for nonequilibrium steady states, demonstrating its validity in heat-conducting quantum systems and introducing a novel entropy concept with time-reversal symmetry.

Contribution

It presents the first quantum mechanical derivation of the extended Clausius relation for nonequilibrium steady states, incorporating genuine quantum dynamics and a new entropy form.

Findings

Extended Clausius relation holds for small temperature differences.

Introduces a quantum entropy with time-reversal symmetrization.

Validates the robustness of classical nonequilibrium thermodynamics concepts in quantum systems.

Abstract

Recently, in their attempt to construct steady state thermodynamics (SST), Komatsu, Nakagwa, Sasa, and Tasaki found an extension of the Clausius relation to nonequilibrium steady states in classical stochastic processes. Here we derive a quantum mechanical version of the extended Clausius relation. We consider a small system of interest attached to large systems which play the role of heat baths. By only using the genuine quantum dynamics, we realize a heat conducting nonequilibrium steady state in the small system. We study the response of the steady state when the parameters of the system are changed abruptly, and show that the extended Clausius relation, in which "heat" is replaced by the "excess heat", is valid when the temperature difference is small. Moreover we show that the entropy that appears in the relation is similar to von Neumann entropy but has an extra symmetrization with respect to time-reversal. We believe that the present work opens a new possibility in the study of nonequilibrium phenomena in quantum systems, and also confirms the robustness of the approach by Komtatsu et al.