Stochastic entropy production: Fluctuation relation and irreversibility mitigation in non-unital quantum dynamics

TL;DR

This paper investigates stochastic entropy production in non-unital quantum systems, deriving fluctuation relations and exploring irreversibility mitigation during thermalization processes.

Contribution

It introduces a fluctuation relation for entropy production in non-unital quantum maps and connects it to non-equilibrium potential and relative entropy.

Findings

Derived a fluctuation relation for entropy production.

Expressed average entropy production using relative entropies.

Analyzed irreversibility mitigation in non-Markovian qubit thermalization.

Abstract

In this work, we study the stochastic entropy production in open quantum systems whose time evolution is described by a class of non-unital quantum maps. In particular, as in [Phys. Rev. E 92, 032129 (2015)], we consider Kraus operators that can be related to a nonequilibrium potential. This class accounts for both thermalization and equilibration to a non-thermal state. Unlike unital quantum maps, non-unitality is responsible for an unbalance of the forward and backward dynamics of the open quantum system under scrutiny. Here, concentrating on observables that commute with the invariant state of the evolution, we show how the non-equilibrium potential enters the statistics of the stochastic entropy production. In particular, we prove a fluctuation relation for the latter and we find a convenient way of expressing its average solely in terms of relative entropies. Then, the theoretical results are applied to the thermalization of a qubit with non-Markovian transient, and the phenomenon of irreversibility mitigation, introduced in [Phys. Rev. Research 2, 033250 (2020)], is analyzed in this context.