Conservation of local equilibrium for attractive particle systems on \(Z^ d\)
type: Item
instance of: scholarly article
title: Conservation of local equilibrium for attractive particle systems on \(Z^ d\)
zbMATH Open document ID: 0798.60085
published in: The Annals of Probability
publication date: 1994-04-18T00:00:00Z
review text: It is generally expected, that in the hydrodynamic limit local equilibrium holds, i.e. at each time in microscopic neighbourhoods of each macroscopic point the system is approximately in equilibrium. This local equilibrium is characterized by macroscopic parameters depending on time and space, which evolve according to a partial differential equation, the hydrodynamic or Euler equation. In this second paper conservation of local equilibrium is proved for attractive particle systems with one macroscopic equilibrium parameter, the density, if a law of large numbers holds for the density field and under regularity assumptions on the hydrodynamic equation. This theorem is applied to zero range and symmetric simple exclusion processes. The above announced paper is a predecessor, which treats the asymmetric zero range process for special initial profiles with more specific methods.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 528621
zbMATH Keywords: particle systems
zbMATH Keywords: hydrodynamic limit
zbMATH Keywords: local equilibrium
zbMATH Keywords: zero range process
zbMATH Keywords: simple exclusion process
author: C. Landim
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176989000
OpenAlex ID: W2013067041
DOI: 10.1214/AOP/1176989000
description: scientific article; zbMATH DE number 528621