Hydrodynamical Behavior for the Symmetric Simple Partial Exclusion with Open Boundary

We analyze the symmetric simple partial exclusion process, which allows at most \(\alpha \) particles per site, and we put it in contact with stochastic reservoirs whose strength is regulated by a parameter \(\theta \in {\mathbb {R}}\). We prove that the hydrodynamic behavior is given by the heat equation and depending on the value of \(\theta \), the equation is supplemented with different boundary conditions. Setting \(\alpha = 1\) we find the results known in Baldasso et al. (J Stat Phys 167(5):1112–1142, 2017) and Bernardin et al. (Markov Processes Relat. Fields 25:217–274, 2017) for the symmetric simple exclusion process.