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arXiv:1706.00341 · Physical Review Letters

No Thermalization without Correlations

Dmitry V. Zhdanov, Denys I. Bondar, Tamar Seideman

Published Oct 24, 2017• 10 citations
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Abstract

The proof of the long-standing conjecture is presented that Markovian quantum master equations are at odds with quantum thermodynamics under conventional assumptions of fluctuation-dissipation theorems (implying a translation invariant dissipation). Specifically, except for identified systems, persistent system-bath correlations of at least one kind, spatial or temporal, are obligatory for thermalization. A systematic procedure is proposed to construct translation invariant bath models producing steady states that well approximate thermal states. A quantum optical scheme for the laboratory assessment of the developed procedure is outlined.

DOI
10.1103/physrevlett.119.170402

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The proof of the long-standing conjecture is presented that Markovian quantum master equations are at odds with quantum thermodynamics under conventional assumptions of fluctuation-dissipation theorems (implying a translation invariant dissipation). Specifically, except for identified systems, persistent system-bath correlations of at least one kind, spatial or temporal, are obligatory for thermalization. A systematic procedure is proposed to construct translation invariant bath models producing steady states that well approximate thermal states. A quantum optical scheme for the laboratory assessment of the developed procedure is outlined.
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Periodically driven open quantum systems are central to quantum thermodynamics and quantum control. These systems are typically described using Floquet-Born-Markov master equations, derived with the use of a full secular approximation, and whose thermodynamic implications are often overlooked. In this context, we show that such a strong secular approximation may lead to unphysical predictions for steady state energy currents. We then demonstrate that a coarse-grained formulation of the master equation can regularize these issues while yielding completely positive dynamics and consistent energy currents. The coarse-graining time has a clear physical interpretation, as it defines the temporal resolution at which a Markovian master equation can describe the evolution of the periodically driven system. We show the consistency and validity of our approach by comparing to an exact non-Markovian simulation in paradigmatic examples: a driven two-level system and a three-level maser coupled to hot and cold thermal reservoirs. Our work provides a practical framework for correctly applying the secular approximation in periodically driven-dissipative systems and for assessing the accuracy of master equations of the GKSL form.
Markovian quantum master equations (MQMEs) were established nearly half a century ago. They have often been used in the study of irreversible thermodynamics. However, the previous results were mainly concerned about ensemble averages; the stochastic thermodynamics of these systems went unnoticed for a very long time. This situation remained unchanged until a variety of fluctuation theorems in classical and quantum regimes were found in the past two decades. In this paper, we systematically summarize the current understanding on the stochastic heat and work in MQMEs using two distinct strategies. One strategy is to treat the system and its surrounding heat bath as a closed quantum system, to suppose that the evolution of the composite system is unitary under a time-dependent total Hamiltonian and to define the heat and work as the changes in energy by applying two energy measurements scheme to the composite system. The other strategy is to unravel these MQMEs into random quantum jump trajectories (QJTs) and to define the stochastic heat and work along the individual trajectories. Many important physical concepts, mathematical techniques, and fluctuation theorems at different descriptive levels are given in as detailed a manner as possible. We also use concrete models to illustrate these results.