A test of "fluctuation theorem" in non-Markovian open quantum systems

TL;DR

This paper extends the fluctuation theorem to non-Markovian open quantum systems, demonstrating its validity through numerical simulations of the spin-boson model and analyzing entropy production.

Contribution

It generalizes the fluctuation theorem to non-Markovian quantum systems with Gaussian heat baths, expanding its applicability beyond Markovian cases.

Findings

Detailed balance holds in non-Markovian regimes except during strong transients.

The generalized entropy production remains valid in wide parameter regions.

Numerical simulations support the theoretical extension of fluctuation theorems.

Abstract

We study fluctuation theorems for open quantum systems with a non-Markovian heat bath using the approach of quantum master equations and examine the physical quantities that appear in those fluctuation theorems. The approach of Markovian quantum master equations to the fluctuation theorems was developed by Esposito and Mukamel [Phys. Rev. E {\bf73}, 046129 (2006)]. We show that their discussion can be formally generalized to the case of a non-Markovian heat bath when the local system is linearly connected to a Gaussian heat bath with the spectrum distribution of the Drude form. We found by numerically simulating the spin-boson model in non-Markovian regime that the "detailed balance" condition is well satisfied except in a strongly non-equilibrium transient situation, and hence our generalization of the definition of the "entropy production" is almost always legitimate. Therefore, our generalization of the fluctuation theorem seems meaningful in wide regions.