Free energy functional for nonequilibrium systems: an exactly solvable case.
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.
Derrida
B
B
Laboratoire de Physique Statistique, 24 rue Lhomond, 75231 Paris Cedex 05, France. derrida@lps.ens.fr
Lebowitz
J L
JL
Speer
E R
ER