周期驱动马氏链中熵产生和热耗散的涨落定理
Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains
摘要：
渐近涨落定理是一个过程的时间平均熵产生或热耗散的速率函数中的Gallavotti-Cohen对称性的陈述。这样的定理已经被证明为各种一般类的连续时间确定性和随机过程，但总是在假设驱动系统的力是时间无关的，往往依赖于存在一个限制遍历分布。在本文中，我们扩展的渐近波动定理的第一次非齐次连续时间过程没有平稳分布，特别是考虑有限状态马尔可夫链驱动的周期性转移率。我们发现，对于熵产生和热耗散，通常的Gallavotti-Cohen对称性的速率函数被推广到一个类似的关系之间的原始过程和相应的向后的过程，其中的轨迹和驱动协议已被时间反转的速率函数。其结果是，在向前过程中，每个量的长时间平均值的自发正波动比向后过程中的自发负波动更有可能呈指数级增长，反之亦然，揭示了时间向前和向后移动的宇宙中波动的分布是相关的。作为一个额外的结果，渐近的时间平均熵产生作为周期性的熵产生率的积分，推广有关均匀动力学的常数速率。
英文摘要：
Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-reversed. The effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process, and vice-versa, revealing that the distributions of fluctuations in universes in which time moves forward and backward are related. As an additional result, the asymptotic time-averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics.
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