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Stationary measures and hydrodynamics of zero range processes with several species of particles
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Grosskinsky, Stefan and Spohn, Herbert (2003) Stationary measures and hydrodynamics of zero range processes with several species of particles. Bulletin of the Brazilian Mathematical Society, Vol.34 (No.3). pp. 489-507. doi:10.1007/s00574-003-0026-z ISSN 1678-7714.
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Official URL: http://dx.doi.org/10.1007/s00574-003-0026-z
Abstract
We study general zero range processes with different types of particles on a ddimensional
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Particles -- Mathematical models, Stochastic systems | ||||
Journal or Publication Title: | Bulletin of the Brazilian Mathematical Society | ||||
Publisher: | Springer | ||||
ISSN: | 1678-7714 | ||||
Official Date: | 2003 | ||||
Dates: |
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Volume: | Vol.34 | ||||
Number: | No.3 | ||||
Page Range: | pp. 489-507 | ||||
DOI: | 10.1007/s00574-003-0026-z | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 16 December 2015 | ||||
Date of first compliant Open Access: | 16 December 2015 | ||||
Funder: | Institut Henri Poincaré, Deutscher Akademischer Austauschdienst (DAAD), Brazil. Coordenação do Aperfeiçoamento de Pessoal de Nível Superior (CAPES) |
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