Large Deviation of the Density Profile in the Steady State of the Open Symmetric Simple Exclusion Process View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2002-05

AUTHORS

B. Derrida, J. L. Lebowitz, E. R. Speer

ABSTRACT

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. More... »

PAGES

599-634

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1014555927320

DOI

http://dx.doi.org/10.1023/a:1014555927320

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009911887


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