Abstract

In ergodic physical systems, time-averaged quantities converge (for large times) to their ensemble-averaged values. Large deviation theory describes rare events where these time averages differ significantly from the corresponding ensemble averages. It allows estimation of the probabilities of these events, and their mechanisms. This theory has been applied to a range of physical systems, where it has yielded new insights into entropy production, current fluctuations, metastability, transport processes, and glassy behaviour. We review some of these developments, identifying general principles. We discuss a selection of dynamical phase transitions, and we highlight some connections between large-deviation theory and optimal control theory.

Graphical abstract

中文翻译：

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具有随机动力学的物理系统的遍历性和大偏差

摘要

在遍历物理系统中，时间平均量（长时间）收敛到其整体平均值。大偏差理论描述了罕见事件，其中这些时间平均值与相应的整体平均值明显不同。它允许估计这些事件的概率及其机制。该理论已被应用到一系列物理系统中，在其中产生了对熵产生，电流波动，亚稳性，传输过程和玻璃态行为的新见解。我们回顾了其中的一些进展，确定了一般原则。我们讨论了动态相变的选择，并且重点介绍了大偏差理论和最优控制理论之间的一些联系。

图形概要