EPJ B Colloquium - Ergodicity and large deviations in physical systems with stochastic dynamics

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Published on 22 April 2020

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, and has been applied to a wide range of physical systems, including exclusion processes, glassy materials, models of heat transport, proteins, climate models, and non-equilibrium quantum systems.

In a new Colloquium article published in EPJB, Dr Robert Jack (University of Cambridge, UK) outlines the application of large deviation theory to these systems, where it has yielded fresh insights into entropy production, current fluctuations, metastability, transport processes, and glassy behaviour. The article covers some recent developments and identifies general principles, discussing a selection of dynamical phase transitions, and highlighting some connections between large-deviation theory and optimal control theory.