Exact Large Deviation Functional of a Stationary Open Driven Diffusive System: The Asymmetric Exclusion Process View Full Text


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Article Info

DATE

2003-03

AUTHORS

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

ABSTRACT

We consider the asymmetric exclusion process (ASEP) in one dimension on sites i=1,...,N, in contact at sites i=1 and i=N with infinite particle reservoirs at densities ρa and ρb. As ρa and ρb are varied, the typical macroscopic steady state density profile ¯ρ(x), x∈[a,b], obtained in the limit N=L(b−a)→∞, exhibits shocks and phase transitions. Here we derive an exact asymptotic expression for the probability of observing an arbitrary macroscopic profile , so that is the large deviation functional, a quantity similar to the free energy of equilibrium systems. We find, as in the symmetric, purely diffusive case q=1 (treated in an earlier work), that is in general a non-local functional of ρ(x). Unlike the symmetric case, however, the asymmetric case exhibits ranges of the parameters for which is not convex and others for which has discontinuities in its second derivatives at ρ(x)=¯ρ(x). In the latter ranges the fluctuations of order in the density profile near ¯ρ(x) are then non-Gaussian and cannot be calculated from the large deviation function. More... »

PAGES

775-810

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1022111919402

DOI

http://dx.doi.org/10.1023/a:1022111919402

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1027227376


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