Large deviations of the empirical current for the boundary driven Kawasaki process with long range interaction

2014/06/05 by Mustapha Mourragui, Mourragui, Mustapha · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Material Dynamics and Properties #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1406.1463

openalex publication_date 2014/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a lattice gas evolving in a bounded cylinder of length 2N + 1 and interacting via a Neuman Kac interaction of range N, in contact with particles reservoirs at different densities. We investigate the associated law of large numbers and large deviations of the empirical current and of the density. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by a nonlocal, nonlinear evolution equation with Dirichlet boundary conditions.

Citations

• On the van der Waals Theory of the Vapor-Liquid Equilibrium. I. Discussion of a One-Dimensional Model

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