We study work extraction processes mediated by finite-time interactions with an ambient bath—partial thermalizations—as continuous-time Markov processes for two-level systems. Such a stochastic process results in fluctuations in the amount of work that can be extracted and is characterized by the rate at which the system parameters are driven in addition to the rate of thermalization with the bath. We analyze the distribution of work for the case in which the energy gap of a two-level system is driven at a constant rate. We derive analytic expressions for average work and a lower bound for the variance of work showing that such processes cannot be fluctuation-free in general. We also observe that an upper bound for the Monte Carlo estimate of the variance of work can be obtained using Jarzynski's fluctuation-dissipation relation for systems initially in equilibrium. Finally, we analyze work extraction cycles by modifying the Carnot cycle, incorporating processes involving partial thermalizations, and we obtain efficiency at maximum power for such finite-time work extraction cycles under different sets of constraints.

中文翻译：

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两级系统中由于部分热化而导致的工作波动

我们研究了与环境熔池的有限时间相互作用（部分热化）介导的工作提取过程-作为两级系统的连续时间马尔可夫过程。这样的随机过程导致可提取的工作量的波动，并且其特征在于，除了浴的热化速率外，还以驱动系统参数的速率为特征。对于两级系统的能隙以恒定速率驱动的情况，我们分析了功的分布。我们推导出了平均功的解析表达式，并得出了工作方差的下限，表明这种过程通常不能无波动。我们还观察到，对于最初处于平衡状态的系统，可以使用Jarzynski的涨落-耗散关系来获得功方差的蒙特卡洛估计的上限。最后，我们通过修改卡诺（Carnot）周期来分析工作提取周期，