Entropy of Open Lattice Systems

Details Entropy of Open Lattice Systems Entropy of Open Lattice Systems

2007-04-27

arxiv.org/abs/0704.3742v1

J. Stat. Phys. 126, 1083-1108 (2007)

Physics

Condensed Matter

Statistical Mechanics

Latex, 28 pages, 4 figures as eps files

Scientific paper

We investigate the behavior of the Gibbs-Shannon entropy of the stationary nonequilibrium measure describing a one-dimensional lattice gas, of L sites, with symmetric exclusion dynamics and in contact with particle reservoirs at different densities. In the hydrodynamic scaling limit, L to infinity, the leading order (O(L)) behavior of this entropy has been shown by Bahadoran to be that of a product measure corresponding to strict local equilibrium; we compute the first correction, which is O(1). The computation uses a formal expansion of the entropy in terms of truncated correlation functions; for this system the k-th such correlation is shown to be O(L^{-k+1}). This entropy correction depends only on the scaled truncated pair correlation, which describes the covariance of the density field. It coincides, in the large L limit, with the corresponding correction obtained from a Gaussian measure with the same covariance.

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