Abstract
We study a limit cycle of a quantum Otto engine whose every cycle consists of two finite-time quantum isochoric (heating or cooling) processes and two quantum adiabatic work-extracting processes. Considering a two-level system as a working substance that weakly interacts with two reservoirs comprising an infinite number of bosons, we investigate the non-Markovian effect [short-time behavior of the reduced dynamics in the quantum isochoric processes (QIPs)] on work extraction after infinite repetition of the cycles. We focus on the parameter region where energy transferred to the reservoir can come back to the system in a short-time regime, which we call energy backflow to show partial quantum-mechanical reversibility. As a situation completely different from macroscopic thermodynamics, we find that the interaction energy is finite and negative by evaluating the average energy change of the reservoir during the QIPs by means of the full-counting statistics, corresponding to the two-point measurements. This feature leads us to the following findings: (1) The Carnot theorem is consistent with a definition of work including the interaction energy, although the commonly used definition of work excluding the interaction leads to a serious conflict with the thermodynamic law, and (2) the energy backflow can increase the work extraction. Our findings show that we need to pay attention to the interaction energy in designing a quantum Otto engine operated in a finite time, which requires us to include the non-Markovian effect, even when the system-reservoir interaction is weak.2 MoreReceived 5 June 2020Accepted 29 March 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023078Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum statistical mechanicsQuantum thermodynamicsPhysical SystemsQuantum heat engines & refrigeratorsTechniquesNon-Markovian processesStatistical PhysicsGeneral Physics
Highlights
We have examined the role of the system-reservoir interaction in the non-Markovian quantum Otto engine
While the energy cost of detaching the system from the reservoir caused by the interaction is neglected in the conventional definition of the extracted work in a quantum heat engine, we find that the energy of the system-reservoir interaction temporally changes to be negative during each quantum isochoric process in the non-Markovian quantum Otto engine
By introducing a new definition of work including the interaction energy, we show that the net amount of extracted work remains negative if the parameters are chosen such that the Otto efficiency ηO exceeds the Carnot efficiency ηC
Summary
The quantum heat engine (QHE) is becoming an important topic of interest from various perspectives: (i) It is expected to retrieve and convert wasted heat in quantum devices into energy for work, which may thereby seed another industrial revolution; and (ii) it may offer a deeper understanding of thermodynamics from a quantum point of view. Open-system dynamics of a quantum working substance can be non-Markovian if the time scale of the working substance is comparable to or much shorter than that of the heat reservoirs, invalidating the application of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) treatment [68,69] commonly used in conventional studies. By introducing a definition of work including the interaction, we show that one cannot extract positive work from the non-Markovian QOE operated beyond the Carnot efficiency, an analysis based on the conventional definition excluding the interaction leads to a possibility of the positive work extraction This indicates that the thermodynamics law is consistent with the inclusion of the interaction in the work. We find that the energy backflow increases the amount of the extracted work to exhibit a maximum for a finite contact duration with reservoirs
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