Journal of Statistical Physics

, 144:1151 | Cite as

Current Reservoirs in the Simple Exclusion Process

  • A. De Masi
  • E. Presutti
  • D. Tsagkarogiannis
  • M. E. Vares


We consider the symmetric simple exclusion process in the interval [−N,N] with additional birth and death processes respectively on (NK,N], K>0, and [−N,−N+K). The exclusion is speeded up by a factor N 2, births and deaths by a factor N. Assuming propagation of chaos (a property proved in a companion paper, De Masi et al., we prove convergence in the limit N→∞ to the linear heat equation with Dirichlet condition on the boundaries; the boundary conditions however are not known a priori, they are obtained by solving a non-linear equation. The model simulates mass transport with current reservoirs at the boundaries and the Fourier law is proved to hold.


Hydrodynamic limits Fourier law Non-linear boundary processes 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • A. De Masi
    • 1
  • E. Presutti
    • 2
  • D. Tsagkarogiannis
    • 2
  • M. E. Vares
    • 3
  1. 1.Dipartimento di MatematicaUniversità di L’AquilaL’AquilaItaly
  2. 2.Dipartimento di MatematicaUniversità di Roma Tor VergataRomaItaly
  3. 3.Centro Brasileiro de Pesquisas FísicasRio de JaneiroBrazil

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