开放系统的微正则功和涨落关系：一个精确可解模型
Microcanonical work and fluctuation relations for an open system: An exactly solvable model
摘要：
我们计算的概率分布的工作的系统与环境相互作用的一个精确可解的模型。感兴趣的系统是一个与时间相关的控制参数的谐振子，环境是由具有任意频率的$N$独立谐振子建模，系统与环境的耦合是双线性的，不一定弱。从微正则分布中采样组合系统和环境的初始条件，并根据规定的协议通过改变控制参数来驱动系统脱离平衡。在无限大环境的极限下，即$N \rightarrow \infty$，我们恢复了非平衡功关系和Crooks涨落关系。此外，微正则Crooks关系的有限环境中进行了验证。最后，我们证明了系统在无限环境极限下的多时间关联函数对于正则系综和微正则系综的等价性。
英文摘要：
We calculate the probability distribution of work for an exactly solvable model of a system interacting with its environment. The system of interest is a harmonic oscillator with a time dependent control parameter, the environment is modeled by $N$ independent harmonic oscillators with arbitrary frequencies, and the system-environment coupling is bilinear and not necessarily weak. The initial conditions of the combined system and environment are sampled from a microcanonical distribution and the system is driven out of equilibrium by changing the control parameter according to a prescribed protocol. In the limit of infinitely large environment, i.e. $N \rightarrow \infty$, we recover the nonequilibrium work relation and Crooks's fluctuation relation. Moreover, the microcanonical Crooks relation is verified for finite environments. Finally, we show the equivalence of multi-time correlation functions of the system in the infinite environment limit for canonical and microcanonical ensembles.
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