In this review, we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spin models undergoing phase-ordering dynamics, diffusion equation, fluctuating interfaces, etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalizations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon various experimental systems as well.

中文翻译：

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非平衡系统中的持久性和首过特性

在这篇综述中，我们讨论了扩展多体非平衡系统中的持久性和相关的首通道特性。从具有一个或几个自由度的简单系统开始，例如随机游走和随机加速问题，我们逐步讨论具有多个自由度的系统中的持久性属性。这些系统包括经历相序动力学、扩散方程、波动界面等的自旋模型。在这些系统中，由于有效的潜在随机过程是非马尔可夫的，因此持久性属性非常重要。如本文所述，在过去的二十年中，已经开发了几种精确和近似的方法来计算此类非马尔可夫过程的持久性。我们还讨论了本地站点持久性概率的各种概括。简要讨论了淬灭无序系统中的持久性。虽然这篇评论的主要重点是关于持久性的理论发展，但我们也简要介绍了各种实验系统。