量子Bochkov-Kuzovlev功涨落定理
Quantum Bochkov-Kuzovlev Work Fluctuation Theorems
摘要：
量子版的Bochkov-Kuzovlev恒等式是基于功的适当定义而导出的，功是在给定的协议对系统施加外部作用的开始和结束时测量的量子系统的内能之差。根据最初的Bochkov-Kuzovlev方法的精神，我们采用了“排他性”观点，这意味着与外部工作源的耦合{ \it not}算作内能的一部分。相应的正则和微正则量子涨落定理的推导以及，并进行比较，在“包容性”的方法得到的相应的定理。讨论并阐明了量子包含功$w$、排它功$w_0$和耗散功$w_{dis}$之间的关系。我们通过一个明确的例子表明，$w_0$和$w_{dis}$是不同的随机量服从不同的统计。
英文摘要：
The quantum version of the Bochkov-Kuzovlev identity is derived on the basis of the appropriate definition of work as the difference of the measured internal energies of a quantum system at the beginning and at the end of an external action on the system given by a prescribed protocol. According to the spirit of the original Bochkov-Kuzovlev approach, we adopt the "exclusive" viewpoint, meaning that the coupling to the external work-source is {\it not} counted as part of the internal energy. The corresponding canonical and microcanonical quantum fluctuation theorems are derived as well, and are compared to the respective theorems obtained within the "inclusive" approach. The relations between the quantum inclusive-work $w$, the exclusive-work $w_0$ and the dissipated-work $w_{dis}$, are discussed and clarified. We show by an explicit example that $w_0$ and $w_{dis}$ are distinct stochastic quantities obeying different statistics.
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