Institute of Molecular Physics, Polish Academy of Sciences, ul. M. Smoluchowskiego 17, 60-179 Poznań, Poland.
Phys Rev E. 2018 Jan;97(1-1):012127. doi: 10.1103/PhysRevE.97.012127.
Fluctuations in stochastic systems are usually characterized by full counting statistics, which analyzes the distribution of the number of events taking place in the fixed time interval. In an alternative approach, the distribution of the first-passage times, i.e., the time delays after which the counting variable reaches a certain threshold value, is studied. This paper presents the approach to calculate the first-passage time distribution in systems in which the analyzed current is associated with an arbitrary set of transitions within the Markovian network. Using this approach, it is shown that when the subsequent first-passage times are uncorrelated, there exist strict relations between the cumulants of the full counting statistics and the first-passage time distribution. On the other hand, when the correlations of the first-passage times are present, their distribution may provide additional information about the internal dynamics of the system in comparison to the full counting statistics; for example, it may reveal the switching between different dynamical states of the system. Additionally, I show that breaking of the fluctuation theorem for first-passage times may reveal the multicyclic nature of the Markovian network.
随机系统中的涨落通常可以用全计数统计来描述，它分析了在固定时间间隔内发生事件的数量分布。在另一种方法中，研究了首次通过时间的分布，即计数变量达到某个阈值后的时间延迟。本文提出了一种计算分析电流与马尔可夫网络中任意一组跃迁相关的系统中的首次通过时间分布的方法。使用这种方法，可以证明当后续首次通过时间是不相关时，全计数统计量的累积量和首次通过时间分布之间存在严格的关系。另一方面，当首次通过时间存在相关性时，与全计数统计量相比，它们的分布可能为系统的内部动力学提供额外的信息；例如，它可能揭示系统在不同动态状态之间的切换。此外，我还表明，首次通过时间的涨落定理的破坏可能揭示马尔可夫网络的多循环性质。
