Stochastic Entropy Production: Fluctuation Relation and Irreversibility Mitigation in Non-unital Quantum Dynamics

Year: 2023

Authors: Fiorelli Eliana; Gherardini Stefano; Marcantoni Stefano

Autors Affiliation: Inst Fis Interdisciplinar & Sistemas Complejos IFI, UIB CSIC UIB Campus, Palma De Mallorca 07122, Spain; CNR, Ist Nazl Ott, Area Sci Pk, I-34149 Trieste, Italy; Univ Florence, LENS, Via Carrara 1, I-50019 Sesto Fiorentino, Italy; Abdus Salam Int Ctr Theoret Phys ICTP, Str Costiera 11, I-34151 Trieste, Italy; Univ Nottingham, Sch Phys & Astron, Nottingham NG7 2RD, England; Univ Nottingham, Ctr Math & Theoret Phys Quantum Nonequilibrium Sys, Nottingham NG7 2RD, England; SISSA, Math Area, Via Bonomea 265, I-34136 Trieste, Italy.

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 Res 2:033250 (2020), is analyzed in this context.

Journal/Review: JOURNAL OF STATISTICAL PHYSICS

Volume: 190 (6)      Pages from:   to:

More Information: We acknowledge financial support from The Blanceflor Foundation through the project “The theRmodynamics behInd thE meaSuremenT postulate of quantum mEchanics (TRIESTE)”, from the MISTI Global Seed Funds MIT-FVG Collaboration Grant”Non-Equilibrium Thermodynamics of Dissipative Quantum Systems (NETDQS)”, from the EPSRC through the Grant No. EP/R04421X/1, from the European Research Council through the ERC Starting Grant MaMBoQ (No. 802901) from the PNRR MUR project PE0000023-NQSTI and from the QUARESC project PID2019-109094GB-C21 (AEI /10.13039/501100011033). This work was performed under the auspices of GNFM-INDAM.
KeyWords: Stochastic entropy production, Fluctuation relation, Irreversibility mitigation, Non-unital quantum dynamics
DOI: 10.1007/s10955-023-03118-2

Citations: 1
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