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Hydrodynamical behavior for the generalized symmetric exclusion with open boundary
Chiara Franceschini, Patrícia Gonçalves, Beatriz Salvador · 2022-01-25 · via math.PR updates on arXiv.org

We analyze the generalized symmetric exclusion process, which allows at most $α$ particles per site, and we put it in contact with stochastic reservoirs whose strength is regulated by a parameter $θ\in\mathbb R$. We prove that the hydrodynamic behavior is given by the heat equation and depending on the value of $θ$, the equation is supplemented with different boundary conditions. Setting $α= 1$ we find the results known in [1] for the symmetric simple exclusion process.

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