Exact Free Energy Functional for a Driven Diffusive Open Stationary Nonequilibrium System

TL;DR

This paper derives the exact nonequilibrium free energy functional for a driven diffusive system in a stationary state, revealing nonlocality, phase transitions, and non-Gaussian fluctuations.

Contribution

It provides the first exact form of the free energy functional for a driven open system, highlighting its nonlocal structure and relation to phase transitions.

Findings

Exact probability distribution for density profiles obtained

Reveals non-convexity and discontinuities in free energy functional

Shows non-Gaussian fluctuations in the steady state

Abstract

We obtain the exact probability $\exp[-L {\cal F}(\{\rho(x)\})]$ of finding a macroscopic density profile $\rho(x)$ in the stationary nonequilibrium state of an open driven diffusive system, when the size of the system $L \to \infty$. $\cal F$, which plays the role of a nonequilibrium free energy, has a very different structure from that found in the purely diffusive case. As there, $\cal F$ is nonlocal, but the shocks and dynamic phase transitions of the driven system are reflected in non-convexity of $\cal F$, in discontinuities in its second derivatives, and in non-Gaussian fluctuations in the steady state.