Singularities in large deviation functions

TL;DR

This paper reviews the occurrence of singularities in large deviation functions across equilibrium and non-equilibrium systems, highlighting their classification and differences in finite and infinite-dimensional models.

Contribution

It provides a unified framework for understanding and classifying singularities in large deviation functions in both finite and infinite-dimensional systems.

Findings

Singularities are present in both finite and infinite-dimensional systems.

A classification scheme for singularities is proposed.

Differences between equilibrium and non-equilibrium singularities are discussed.

Abstract

Large deviation functions of configurations exhibit very different behaviors in and out of thermal equilibrium. In particular, they exhibit singularities in a broad range of non-equilibrium models, which are absent in equilibrium. These singularities were first identified in finite-dimensional systems in the weak-noise limit. Recent studies have shown that they are also present in driven diffusive systems with an infinite-dimensional configuration space. This short review describes singularities appearing in both types of systems under a unified framework, presenting a classification of singularities into two broad categories. The types of singularities which were identified for finite-dimensional cases are compared to those found in driven diffusive systems.