Entropy of Open Lattice Systems

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 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.

Latex, 28 pages, 4 figures as eps files

References in corpus (1)

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

Cited by in corpus (28)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Macroscopic fluctuation theory
• Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
• Microscopic versus macroscopic approaches to non-equilibrium systems
• Duality for stochastic models of transport
• Open Quantum Symmetric Simple Exclusion Process
• Long range correlations and phase transition in non-equilibrium diffusive systems
• Entanglement structure of current-driven diffusive fermion systems
• A diffusive system driven by a battery or by a smoothly varying field
• Correlations of the density and of the current in non-equilibrium diffusive systems
• Exact solution of an integrable non-equilibrium particle system
• Large deviations in the symmetric simple exclusion process with slow boundaries
• Eigenstates of triangularisable open XXX spin chains and closed-form solutions for the steady state of the open SSEP
• Exact Entanglement in the Driven Quantum Symmetric Simple Exclusion Process
• Anomalous Fourier's law and long range correlations in a 1D non-momentum conserving mechanical model
• Weakly Non-Equilibrium Properties of Symmetric Inclusion Process with Open Boundaries
• Entropy of stationary nonequilibrium measures of boundary driven symmetric simple exclusion processes
• Duality in quantum transport models
• Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations
• Anomalous long-range correlations at a non-equilibrium phase transition
• Large deviations for out of equilibrium correlations in the symmetric simple exclusion process
• Finite size corrections to the large deviation function of the density in the one dimensional symmetric simple exclusion process
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Entropy of non-equilibrium stationary measures of boundary driven TASEP
• The inclusion process: duality and correlation inequalities
• Stochastic micromodel of the Couette flow
• On Decay of Correlations for Exclusion Processes with Asymmetric Boundary Conditions