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

Abstract

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 Guo, Papanicolaou and Varadhan. We also derive the hydrostatic limit for this model, whose proof is based on the method developed by Landim and Tsunoda. We observe that we do not make use of correlation estimates in none of our results.

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• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Exclusion process with slow boundary
• Hydrodynamics of Porous Medium Model with slow reservoirs
• Non equilibrium stationary state for the SEP with births and deaths
• Hydrodynamic limit of boundary driven exclusion processes with nonreversible boundary dynamics
• Stationary states of boundary driven exclusion processes with nonreversible boundary dynamics
• Hydrodynamics for SSEP with non-reversible slow boundary dynamics: Part II, below the critical regime

Cited by in corpus (5)

• Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics
• Current fluctuations in a semi-infinite line
• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
• Thermodynamics of nonequilibrium driven diffusive systems in mild contact with boundary reservoirs
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond