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arXiv:1604.03476 · Physical review. E

Memory effect in the upper bound of the heat flux induced by quantum fluctuations

Tomoi Koide C

Published Oct 28, 2016• 4 citations
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Abstract

Thermodynamic behaviors in a quantum Brownian motion coupled to a classical heat bath is studied. We then define a heat operator by generalizing the stochastic energetics and show the energy balance (first law) and the upper bound of the expectation value of the heat operator (second law). We further find that this upper bound depends on the memory effect induced by quantum fluctuations and hence the maximum extractable work can be qualitatively modified in quantum thermodynamics.

DOI
10.1103/physreve.94.042140

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Thermodynamic behaviors in a quantum Brownian motion coupled to a classical heat bath is studied. We then define a heat operator by generalizing the stochastic energetics and show the energy balance (first law) and the upper bound of the expectation value of the heat operator (second law). We further find that this upper bound depends on the memory effect induced by quantum fluctuations and hence the maximum extractable work can be qualitatively modified in quantum thermodynamics.
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Quantum systems strongly coupled to many-body systems equilibrate to the reduced state of a global thermal state, deviating from the local thermal state of the system as it occurs in the weak-coupling limit. Taking this insight as a starting point, we study the thermodynamics of systems strongly coupled to thermal baths. First, we provide strong-coupling corrections to the second law applicable to general systems in three of its different readings: As a statement of maximal extractable work, on heat dissipation, and bound to the Carnot efficiency. These corrections become relevant for small quantum systems and vanish in first order in the interaction strength. We then move to the question of power of heat engines, obtaining a bound on the power enhancement due to strong coupling. Our results are exemplified on the paradigmatic non-Markovian quantum Brownian motion.
Quantum-induced stochastic dynamics arises when a quantum system, strongly decohered by its coupling to a quantum environment, evolves as a genuine classical stochastic process. Depending on the environment's quantum state, the environment can act as a dynamic bath, capable of simultaneously exchanging heat and performing work. We formulate a thermodynamic framework for this semiclassical regime, defining heat, work, and entropy production. We derive a modified Second Law that accounts for nonequilibrium quantum features, such as squeezing. The framework is exemplified by an optomechanical setup, where we characterize the thermodynamics of the nonstationary noise induced by the cavity field.
Quantum-Induced Stochastic Dynamics arises from the coupling between a classical system and a quantum environment. Unlike standard thermal reservoirs, this environment acts as a dynamic bath, capable of simultaneously exchanging heat and performing work. We formulate a thermodynamic framework for this semi-classical regime, defining heat, work, and entropy production. We derive a modified Second Law that accounts for non-equilibrium quantum features, such as squeezing. The framework is exemplified by an optomechanical setup, where we characterize the thermodynamics of the non-stationary noise induced by the cavity field.
We establish an upper bound on extractable work for time-dependent, non-Markovian quantum heat engines operating with finite baths. This bound analytically isolates the distinct thermodynamic penalties arising from system-bath correlations, bath non-equilibrium, and residual interaction energy. Evaluating this framework operationally via a quantum polytropic cavity-optomechanical cycle, we demonstrate that maximal efficiency requires quasi-static operation to successfully harvest coherent, non-Markovian system-bath resonances. Conversely, optimising for maximum power enforces a strict finite-time regime. Under realistic hardware constraints, this acceleration necessitates larger discrete operational steps, where we expect Trotterisation errors to manifest as physical noise. Such noise would irreversibly suppress delicate quantum memory effects, forcing a collapse to the memoryless Markovian Otto limit. Coupled with the permanent energetic tax of switching finite-bath interactions, our results indicate that the exploitation of quantum memory resources and finite-power operation belong to different operational regimes.