Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-05-04
Phys. Rev. Lett. 87, Issue 15, 150601 (2001)
Physics
Condensed Matter
Statistical Mechanics
4 pages, RevTeX. Changes: correct minor errors, add reference, minor rewriting requested by editors and referee
Scientific paper
10.1103/PhysRevLett.87.150601
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 $\exp[-N{\cal F}(\{\rho\})]$; ${\cal F}$ thus generalizes to nonequilibrium systems the notion of free energy density for equilibrium systems. Our exact expression for $\cal F$ 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 Bernard
Lebowitz Joel. L.
Speer Eugene R.
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