Current fluctuations in systems with diffusive dynamics, in and out of equilibrium

TL;DR

This paper demonstrates that current fluctuations in diffusive systems exhibit universal features both at equilibrium and out of equilibrium, using a mapping between boundary-driven and equilibrium states for specific models.

Contribution

It establishes a universal mapping between current fluctuations in equilibrium and boundary-driven nonequilibrium diffusive systems, confirmed for two key models.

Findings

Current fluctuations are universal in equilibrium and certain nonequilibrium systems.

A mapping relates out-of-equilibrium fluctuations to equilibrium distributions.

Exact correspondence shown for the Simple Symmetric Exclusion Process and KMP model.

Abstract

For diffusive systems that can be described by fluctuating hydrodynamics and by the Macroscopic Fluctuation Theory of Bertini et al., the total current fluctuations display universal features when the system is closed and in equilibrium. When the system is taken out of equilibrium by a boundary-drive, current fluctuations, at least for a particular family of diffusive systems, display the same universal features as in equilibrium. To achieve this result, we exploit a mapping between the fluctuations in a boundary-driven nonequilibrium system and those in its equilibrium counterpart. Finally, we prove, for two well-studied processes, namely the Simple Symmetric Exclusion Process and the Kipnis-Marchioro-Presutti model for heat conduction, that the distribution of the current out of equilibrium can be deduced from the distribution in equilibrium. Thus, for these two microscopic models, the mapping between the out-of-equilibrium setting and the equilibrium one is exact.