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arXiv:1902.07356 · Physical Review A

Non-Markov enhancement of maximum power for quantum thermal machines

Paolo Abiuso, Vittorio Giovannetti

Published May 6, 2019• 63 citations
arXivHTMLPDF

Abstract

In this work we study how the non-Markovian character of the dynamics can affect the thermodynamic performance of a quantum thermal engine, by analyzing the maximum power output of Carnot and Otto cycles departing from the quasistatic and infinite-time-thermalization regime respectively, introducing techniques for their control optimization in general dynamical models. In our model, non-Markovianity is introduced by allowing some degrees of freedom of the reservoirs to be taken into account explicitly and share correlations with the engine by Hamiltonian coupling. It is found that the non-Markovian effects can fasten the control and improve the power output.

DOI
10.1103/physreva.99.052106

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In this work we study how the non-Markovian character of the dynamics can affect the thermodynamic performance of a quantum thermal engine, by analyzing the maximum power output of Carnot and Otto cycles departing from the quasistatic and infinite-time-thermalization regime respectively, introducing techniques for their control optimization in general dynamical models. In our model, non-Markovianity is introduced by allowing some degrees of freedom of the reservoirs to be taken into account explicitly and share correlations with the engine by Hamiltonian coupling. It is found that the non-Markovian effects can fasten the control and improve the power output.
We use fast periodic control to realize finite-time Otto cycles exhibiting quantum advantage.Such periodic modulation of the working medium-bath interaction Hamiltonian during the thermalization strokes can give rise to non-Markovian anti-Zeno dynamics and corresponding reduction in the thermalization times.Faster thermalization can in turn significantly enhance the power output in engines or, equivalently, the rate of refrigeration in refrigerators.This improvement in performance of dynamically controlled Otto thermal machines arises due to the time-energy uncertainty relation of quantum mechanics.
Abstract We study the performance of a quantum Otto cycle using a harmonic work medium and undergoing collisional dynamics with finite-size reservoirs. We span the dynamical regimes of the work strokes from strongly non-adiabatic to quasi-static conditions, and address the effects that non-Markovianity of the open-system dynamics of the work medium can have on the efficiency of the thermal machine. While such efficiency never surpasses the classical upper bound valid for finite-time stochastic engines, the behaviour of the engine shows clear-cut effects induced by both the finiteness of the evolution time, and the memory-bearing character of the system-environment evolution.
Enhancement of thermal efficiency of quantum heat engines has been discussed mainly in terms of quantumness of working substances. In the present study, we propose as another possibility to utilize a quantum-mechanical (reversible) feature of system-reservoir interaction, which reveals itself in the short-time regime as a non-Markovian effect on the reduced dynamics of the substance, before asymptotically approaching irreversible processes. For this purpose, we study a limit cycle of the quantum Otto engine comprising a working two-level system and two reservoirs, including the non-Markovian effect for the finite-time isochoric processes while the work-extracting processes are kept quantum adiabatic. Assuming that the system interacts weakly with the reservoirs consisting of infinite bosons, we find a parameter regime beyond the Carnot efficiency in which a positive work is extracted by including a non-Markovian effect called energy backflow. We also find that the interaction energy is finite and contributes to the positive work even for the weak interaction. The work diminishes if we include into the work the energy for detaching the working substance from reservoirs.
The extension of quantum thermodynamics to situations that go beyond standard thermodynamic settings comprises an important and interesting aspect of its development. One such situation is the analysis of the thermodynamic consequences of structured environments that induce a non-Markovian dynamics. We study a quantum Otto refrigerator where the standard Markovian cold reservoir is replaced by a specific engineered cold reservoir which may induce a Markovian or non-Markovian dynamics on the quantum refrigerant system. The two dynamical regimes can be interchanged by varying the coupling between the refrigerant and the reservoir. An increase of non-Markovian effects will be related to an increase of the coupling strength, which in turn will make the energy stored in the interaction Hamiltonian, the interaction energy, increasingly relevant. We show how the figures of merit, the coefficient of performance, and the cooling power change for non-negligible interaction energies, discussing how neglecting this effect would lead to an overestimation of the refrigerator performance. Finally, we also consider a numerical simulation of a spin quantum refrigerator with experimentally feasible parameters to better illustrate the non-Markovian effects induced by the engineered cold reservoir. We argue that a moderate non-Markovian dynamics performs better than either a Markovian or a strong non-Markovian regime of operation.
Conventional quantum Otto engines based on effective-negative-temperature reservoirs rely on an assumption of perfect thermalization. In this study, the authors investigate the impact of non-Markovianity in these engines by terminating strokes before reaching thermal equilibrium, revealing that higher non-Markovianity enhances maximum efficiency but reduces overall performance over an extended period of functioning time. The authors also identify a class of effective-negative-temperature-based necessarily transient quantum Otto engines.
Abstract Real quantum heat engines lack the separation of time and length scales that is characteristic for classical engines. They must be understood as open quantum systems in non-equilibrium with time-controlled coupling to thermal reservoirs as integral part. Here, we present a systematic approach to describe a broad class of engines and protocols beyond conventional weak coupling treatments starting from a microscopic modeling. For the four stroke Otto engine the full dynamical range down to low temperatures is explored and the crucial role of the work associated with the coupling/de-coupling to/from reservoirs as an integral part in the energy balance is revealed. Quantum correlations turn out to be instrumental to enhance the efficiency which opens new ways for optimal control techniques.