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Article Dans Une Revue Journal of Statistical Physics Année : 2020

Hydrodynamics for the SSEP with non-reversible slow boundary dynamics: part I, the critical regime and beyond

P Gonçalves
  • Fonction : Auteur
G Nahum
  • Fonction : Auteur

Résumé

The purpose of this article is to provide a simple proof of the hydrodynamic and hydrostatic behavior of the SSEP in contact with slowed reservoirs which inject and remove particles in a finite size windows at the extremities of the bulk. More precisely, the reservoirs inject/remove particles at/from any point of a window of size K placed at each extremity of the bulk and particles are injected/removed to the first open/occupied position in that window. The hydrodynamic limit is given by the heat equation with non-linear Robin boundary conditions or Neumann boundary conditions, the latter being in the case when the reservoirs are too slow. The proof goes through the entropy method of [16]. We also derive the hydrostatic limit for this model, whose proof is based on the method developed in [18] and [20]. We observe that we do not make use of correlation estimates in none of our results.
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Dates et versions

hal-02469043 , version 1 (06-02-2020)

Identifiants

  • HAL Id : hal-02469043 , version 1

Citer

Clément Erignoux, P Gonçalves, G Nahum. Hydrodynamics for the SSEP with non-reversible slow boundary dynamics: part I, the critical regime and beyond. Journal of Statistical Physics, 2020, 181, pp.1433--1469. ⟨hal-02469043⟩
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