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.

中文翻译：

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量子奥托引擎的非马尔可夫效应：系统-储层相互作用的作用

我们研究了一个量子奥托发动机的极限循环，其每个循环都由两个有限时间量子等容（加热或冷却）过程和两个量子绝热功提取过程组成。考虑到一个两级系统作为与包含无限多个玻色子的两个储集层弱相互作用的工作物质，我们研究了工作中的非马尔可夫效应[量子等速过程（QIPs）的减少动力学的短时行为]。无限重复循环后进行提取。我们关注于参数区域，传递到储层的能量可以在短时间内返回系统，我们称其为能量回流，以显示部分量子力学可逆性。与宏观热力学完全不同的情况是，我们通过利用全计数统计方法（对应于两点测量）来评估QIP期间储层的平均能量变化，从而发现相互作用能是有限的且为负的。这一特征使我们得出以下发现：（1）卡诺定理与包括相互作用能的功的定义是一致的，尽管排除相互作用的常用功定义导致与热力学定律的严重冲突，和（2 ）能量回流会增加工作量。我们的发现表明，在设计有限时间内运行的量子奥托发动机时，我们需要注意相互作用能，这要求我们即使在系统-储层相互作用较弱的情况下也要考虑非马尔可夫效应。