Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes
Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes
复制标题
DOI：
10.1103/physrevx.7.011019
复制
发表时间：
2017-02-21
影响因子：
12.5
通讯作者：
Juelicher, Frank
中科院分区：
文献类型：
--
作者：
Neri, Izaak;Roldan, Edgar;Juelicher, Frank
我们研究了非平衡稳态下熵产生的下界、停止时间和通过概率的统计数据，并证明它们是普遍的。我们考虑停止时间的两个例子：熵产生的首次通过时间和随机过程的等待时间，这是系统第一次达到给定状态的时间。我们的主要结果如下：（i）熵产生的全局下确界呈指数分布，均值等于负玻尔兹曼常数； (ii) 我们找到熵产生的通过概率的精确表达式； (iii) 我们推导出熵产生的停止时间分布的涨落定理。这些结果对随机过程具有有趣的意义，可以在简单的胶体系统和活性分子过程中进行讨论。特别是，我们表明分子过程的离散化学转变的时间和统计数据（例如分子马达的步骤）受熵产生的统计数据控制。我们还表明，活跃分子过程的极值统计量受熵产生的控制；例如，我们推导出分子马达相对于外力方向的最大偏移与相应的熵产生波动的下确界之间的关系。利用这种关系，我们对 RNA 聚合酶的最大回溯深度的分布进行预测，这是根据我们对熵产生下限的通用结果得出的。
We study the statistics of infima, stopping times, and passage probabilities of entropy production in nonequilibrium steady states, and we show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches a given state for the first time. Our main results are as follows: (i) The distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmann's constant; (ii) we find exact expressions for the passage probabilities of entropy production; (iii) we derive a fluctuation theorem for stopping-time distributions of entropy production. These results have interesting implications for stochastic processes that can be discussed in simple colloidal systems and in active molecular processes. In particular, we show that the timing and statistics of discrete chemical transitions of molecular processes, such as the steps of molecular motors, are governed by the statistics of entropy production. We also show that the extreme-value statistics of active molecular processes are governed by entropy production; for example, we derive a relation between the maximal excursion of a molecular motor against the direction of an external force and the infimum of the corresponding entropy-production fluctuations. Using this relation, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases, which follow from our universal results for entropy-production infima.