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We consider an open one dimensional lattice gas on sites i=1,..., N, with particles jumping independently with rate 1 to neighboring interior empty sites, the simple symmetric exclusion process. The particle fluxes at the left and right boundaries, corresponding to exchanges with reservoirs at different chemical potentials, create a stationary nonequilibrium state (SNS) with a steady flux of particles through the system. The mean density profile in this state, which is linear, describes the typical behavior of a macroscopic system, i.e., this profile occurs with probability 1 when N→∞. The probability of microscopic configurations corresponding to some other profile ρ(x), x=i/N, has the asymptotic form exp[−N({ρ})]; is the large deviation functional. In contrast to equilibrium systems, for which eq({ρ}) is just the integral of the appropriately normalized local free energy density, the we find here for the nonequilibrium system is a nonlocal function of ρ. This gives rise to the long range correlations in the SNS predicted by fluctuating hydrodynamics and suggests similar non-local behavior of in general SNS, where the long range correlations have been observed experimentally.
2002-05-01
research_article
en
2019-04-10T14:58
2002-05
articles
599-634
Large Deviation of the Density Profile in the Steady State of the Open Symmetric Simple Exclusion Process
http://link.springer.com/10.1023/A:1014555927320
Engineering
J. L.
Lebowitz
E. R.
Speer
Rutgers University
Department of Mathematics, Rutgers University, 08903, New Brunswick, New Jersey
dimensions_id
pub.1009911887
Springer Nature - SN SciGraph project
Derrida
B.
doi
10.1023/a:1014555927320
107
readcube_id
2f384cf2b7cec0bf075fb801c24d5e4690ec34c52cb2d0e95ff46a86198a041f
Journal of Statistical Physics
0022-4715
1572-9613
Laboratoire de Physique Statistique
Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 rue Lhomond, 75005, Paris, France
3-4
Interdisciplinary Engineering