2003/05/14 by Stefan Grosskinsky, Stefan Gro�kinsky, Herbert Spohn · 35 citations
Mathematics · Medicine · Physics and Astronomy · #Boundary value problem #Entropy (arrow of time) #Jump #Kullback–Leibler divergence #Limit (mathematics) #Mathematical and Theoretical Epidemiology and Ecology Models #Particle system #Range (aeronautics) #Regular polygon #Spectral Theory in Mathematical Physics #Stationary solution #Stochastic processes and statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.1007/s00574-003-0026-z
published in Bulletin of the Brazilian Mathematical Society New Series 34(3), 489-507 (Springer Science+Business Media)
arxiv created 2003/05/14 · openalex publication_date 2003/11/01 · openalex created_date 2016/06/24 · arxiv updated 2018/04/26 · openalex updated_date 2026/08/05
We study general zero range processes with different types of particles on a d-dimensional lattice with periodic boundary conditions. A necessary and sufficient condition on the jump rates for the existence of stationary product measures is established. For translation invariant jump rates we prove the hydrodynamic limit on the Euler scale using Yau's relative entropy method. The limit equation is a system of conservation laws, which are hyperbolic and have a globally convex entropy. We analyze this system in terms of entropy variables. In addition we obtain stationary density profiles for open boundaries.