Abstract
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 modeling of transport in mesoscopic systems, consists in using local master equations (LMEs) 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 LMEs 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.
Highlights
The description and manipulation of energy transfer at the quantum scale is a problem of fundamental and technological importance, receiving increasing attention in recent years
Coherent manipulation of energy is at the core of quantum thermodynamics, whose aims include the understanding of the emergence of thermodynamic laws from quantum mechanics [13,14,15,16,17,18,19,20,21] and the design of thermal machines made with quantum devices [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41]
We study the efficiency and/or coefficient of performance (COP) for this model and show that they reach the optimal value of the Otto cycle in the case where the oscillators interact without counter-rotating terms in the Hamiltonian: including counterrotating terms only degrades the operation of the system
Summary
An alternative method, employed especially in the modeling of transport in mesoscopic systems, consists in using local master equations (LMEs) containing Lindblad operators acting locally only on the corresponding subsystem. 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
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