Abstract
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 → ∞, 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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Derrida, B., Lebowitz, J.L. & Speer, E.R. Entropy of Open Lattice Systems. J Stat Phys 126, 1083–1108 (2007). https://doi.org/10.1007/s10955-006-9160-5
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DOI: https://doi.org/10.1007/s10955-006-9160-5