Reconciliation of quantum local master equations with thermodynamics

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    The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases very hard. An alternative method, employed especially in the modelling of transport in mesoscopic systems, consists in using {\it local} master equations containing Lindblad operators acting locally only on the corresponding subsystem. It has been shown that this approach however generates inconsistencies with the laws of thermodynamics. In this paper we demonstrate that using a microscopic model of local master equations based on repeated collisions all thermodynamic inconsistencies can be resolved by correctly taking into account the breaking of global detailed balance related to the work cost of maintaining the collisions. We provide examples based on a chain of quantum harmonic oscillators whose ends are connected to thermal reservoirs at different temperatures. We prove that this system behaves precisely as a quantum heat engine or refrigerator, with properties that are fully consistent with basic thermodynamics.


    • Reconciliation of quantum local master equations with thermodynamics

      Rights statement: Copyright 2018 the authors. This is an open access article published under a Creative Commons Attribution License (, which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.

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    Original languageEnglish
    Pages (from-to)1-17
    JournalNew J. Phys.
    Journal publication date16 Nov 2018
    Early online date16 Nov 2018
    Publication statusEarly online date - 16 Nov 2018

      Research areas

    • quant-ph, cond-mat.stat-mech

    ID: 161093946