Department of Physics and Astronomy "G. Galilei," University of Padova, Padova 35131, Italy.
Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland.
Phys Rev E. 2023 Jan;107(1-1):014129. doi: 10.1103/PhysRevE.107.014129.
Out-of-equilibrium systems continuously generate entropy, with its rate of production being a fingerprint of nonequilibrium conditions. In small-scale dissipative systems subject to thermal noise, fluctuations of entropy production are significant. Hitherto, mean and variance have been abundantly studied, even if higher moments might be important to fully characterize the system of interest. Here, we introduce a graphical method to compute any moment of entropy production for a generic discrete-state system. Then, we focus on a paradigmatic model of active particles, i.e., run-and-tumble dynamics, which resembles the motion observed in several micro-organisms. Employing our framework, we compute the first three cumulants of the entropy production for a discrete version of this model. We also compare our analytical results with numerical simulations. We find that as the number of states increases, the distribution of entropy production deviates from a Gaussian. Finally, we extend our framework to a continuous state-space run-and-tumble model, using an appropriate scaling of the transition rates. The approach presented here might help uncover the features of nonequilibrium fluctuations of any current in biological systems operating out-of-equilibrium.
非平衡系统不断产生熵，其产生率是不平衡条件的特征。在受到热噪声的小规模耗散系统中，熵产生的涨落非常显著。迄今为止，均值和方差已经得到了充分的研究，即使更高阶矩对于全面描述感兴趣的系统可能很重要。在这里，我们引入了一种计算任意阶熵产生矩的图形方法，用于一般的离散状态系统。然后，我们关注一个主动粒子的范例模型，即跑-跌动力学，它类似于在几种微生物中观察到的运动。我们使用我们的框架，为这个模型的离散版本计算了熵产生的前三个累积量。我们还将我们的分析结果与数值模拟进行了比较。我们发现，随着状态数的增加，熵产生的分布偏离高斯分布。最后，我们通过适当的跃迁速率缩放，将我们的框架扩展到连续状态空间的跑-跌模型。这里提出的方法可能有助于揭示在非平衡状态下运行的生物系统中任何电流的非平衡涨落特征。
