Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case

2001/05/31 by Bernard Derrida, B. Derrida, Joel L. Lebowitz +3 · 21 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.87.150601

published as Phys. Rev. Lett. 87, Issue 15, 150601 (2001) · 4 pages, RevTeX. Changes: correct minor errors, add reference, minor rewriting requested by editors and referee

arxiv created 2001/09/19 · openalex publication_date 2001/09/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the steady state of an open system in which there is a flux of matter between two reservoirs at different chemical potentials. For a large system of size N, the probability of any macroscopic density profile rho(x) is exp[-NF([rho])]; F thus generalizes to nonequilibrium systems the notion of free energy density for equilibrium systems. Our exact expression for F is a nonlocal functional of rho, which yields the macroscopically long range correlations in the nonequilibrium steady state previously predicted by fluctuating hydrodynamics and observed experimentally.

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