Quantum Fluctuation Relations for the Lindblad Master Equation

TL;DR

This paper derives quantum fluctuation relations for systems described by Lindblad master equations, extending classical fluctuation theorems to open quantum systems and connecting them to linear response theory.

Contribution

It introduces a general set of quantum fluctuation relations for Lindblad dynamics, including quantum versions of Jarzynski-Hatano-Sasa and Crooks relations, and derives a generalized fluctuation-dissipation theorem.

Findings

Quantum fluctuation relations for Lindblad systems derived.

Connection to classical fluctuation-dissipation theorem established.

Applicable to systems far from equilibrium.

Abstract

An open quantum system interacting with its environment can be modeled under suitable assumptions as a Markov process, described by a Lindblad master equation. In this work, we derive a general set of fluctuation relations for systems governed by a Lindblad equation. These identities provide quantum versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula.