Unifying relation for quantum systems driven out of equilibrium

TL;DR

This paper extends classical fluctuation and response relations to quantum systems, unifying key theorems and deriving generalized entropy relations for nonequilibrium steady states.

Contribution

It introduces a quantum extension of Crooks' relation that unifies fluctuation theorems and response relations, and derives generalized entropy and Green-Kubo formulas for steady states.

Findings

Unified quantum relation for fluctuation and response theorems

Green-Kubo formula expressed via symmetrized correlation functions

Generalized entropy satisfies extended Clausius and Gibbs relations

Abstract

We extend a classical relation by Crooks to quantum systems and show that it unifies the Crooks transient fluctuation theorem and the Kawasaki non-linear response relation, which leads to the standard linear response theory. We also show that the Green-Kubo formula for a system in a steady state driven by a time-independent driving force is always expressed in terms of the symmetrized correlation function for a quantity induced by the driving force and that a generalized entropy for systems in steady heat conduction states satisfies extensions of the Clausius and the Gibbs relations exactly.