Levernier N, Mendes T V, Bénichou O, Voituriez R, Guérin T
Aix Marseille Univ., Université de Toulon, CNRS, CPT, Turing Center for Living Systems, 13009, Marseille, France.
Laboratoire Ondes et Matière d'Aquitaine, University of Bordeaux, Unité Mixte de Recherche 5798, CNRS, F-33400, Talence, France.
Nat Commun. 2022 Sep 9;13(1):5319. doi: 10.1038/s41467-022-32280-6.
Persistence, defined as the probability that a signal has not reached a threshold up to a given observation time, plays a crucial role in the theory of random processes. Often, persistence decays algebraically with time with non trivial exponents. However, general analytical methods to calculate persistence exponents cannot be applied to the ubiquitous case of non-Markovian systems relaxing transiently after an imposed initial perturbation. Here, we introduce a theoretical framework that enables the non-perturbative determination of persistence exponents of Gaussian non-Markovian processes with non stationary dynamics relaxing to a steady state after an initial perturbation. Two situations are analyzed: either the system is subjected to a temperature quench at initial time, or its past trajectory is assumed to have been observed and thus known. Our theory covers the case of spatial dimension higher than one, opening the way to characterize non-trivial reaction kinetics for complex systems with non-equilibrium initial conditions.
持久性，定义为信号在给定观测时间之前未达到阈值的概率，在随机过程理论中起着至关重要的作用。通常，持久性会随着时间以非平凡指数代数衰减。然而，计算持久性指数的一般分析方法不能应用于在施加初始扰动后瞬态弛豫的非马尔可夫系统这种普遍情况。在这里，我们引入一个理论框架，该框架能够非微扰地确定高斯非马尔可夫过程的持久性指数，这些过程具有非平稳动力学，在初始扰动后弛豫到稳态。分析了两种情况：要么系统在初始时刻经历温度猝灭，要么假定其过去的轨迹已被观测到并因此已知。我们的理论涵盖了空间维度大于一的情况，为表征具有非平衡初始条件的复杂系统的非平凡反应动力学开辟了道路。
