Quantum fluctuation theorems in the strong damping limit

TL;DR

This paper derives quantum fluctuation theorems for strongly damped quantum systems using the quantum Smoluchowski equation, extending classical relations to the quantum regime and proposing an experimental test with Josephson junctions.

Contribution

It introduces quantum versions of Crooks, Jarzynski, and Hatano-Sasa relations for overdamped quantum systems, accounting for non-Gibbsian equilibrium distributions.

Findings

Derived quantum Crooks and Jarzynski relations.

Established a quantum Hatano-Sasa relation for nonequilibrium steady states.

Proposed an experimental setup with Josephson junctions to test quantum entropy fluctuations.

Abstract

We consider a driven quantum particle in the strong friction regime described by the quantum Smoluchowski equation. We derive Crooks and Jarzynski type relations for the reduced quantum system by properly generalizing the entropy production to take into account the non-Gibbsian character of the equilibrium distribution. In the case of a nonequilibrium steady state, we obtain a quantum version of the Hatano-Sasa relation. We, further, propose an experiment with driven Josephson junctions that would allow to investigate nonequilibrium entropy fluctuations in overdamped quantum systems.