Cusp singularities in boundary-driven diffusive systems

TL;DR

This paper investigates non-equilibrium boundary-driven diffusive systems, revealing that their large deviations can exhibit cusp singularities, which are analyzed using numerical, analytical, and catastrophe theory methods.

Contribution

It demonstrates that large deviations in these systems can be non-differentiable and characterizes the cusp singularities using Landau free energy and catastrophe theory.

Findings

Large deviations can be non-differentiable in non-equilibrium systems

Cusp singularities are a generic feature of these deviations

Connections are made with finite-dimensional phase space systems

Abstract

Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be non-differentiable, a phenomenon that is unique to non-equilibrium systems, and discuss the types of models which display such singularities.\ The structure of these singularities is found to generically be a cusp, which can be described by a Landau free energy or, equivalently, by catastrophe theory. Connections with analogous results in systems with finite-dimensional phase spaces are drawn.