Hydrodynamics for SSEP with Non-reversible Slow Boundary Dynamics: Part I, the Critical Regime and Beyond

@article{Erignoux2020HydrodynamicsFS,
  title={Hydrodynamics for SSEP with Non-reversible Slow Boundary Dynamics: Part I, the Critical Regime and Beyond},
  author={Cl{\'e}ment Erignoux and P. Gonçalves and G. Nahum},
  journal={Journal of Statistical Physics},
  year={2020}
}
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… 
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We consider macroscopic systems in weak contact with boundary reservoirs and under the action of external fields. We present an explicit formula for the Hamiltonian of such systems, from which we
Hydrodynamic limit of Exclusion Processes with slow boundaries on hypercubes
We study the hydrodynamic limit of SSEP with slow boundaries on hypercubes in dimension at least two. The hydrodynamic limit equation is shown to be a heat equation with three different types of
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of the Bernoulli Society for Mathematical Statistics and Probability Volume Twenty Eight Number Two May 2022
A list of forthcoming papers can be found online at http://www.bernoullisociety.org/index. php/publications/bernoulli-journal/bernoulli-journal-papers CONTENTS 713 BELLEC, P.C. and ZHANG, C.-H.
Hydrodynamics for SSEP with non-reversible slow boundary dynamics: Part II, below the critical regime
The purpose of this article is to provide a simple proof of the hydrodynamic and hydrostatic behavior of the SSEP in contact with reservoirs which inject and remove particles in a finite size windows

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