  We analyze the generalized symmetric 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 [1] for
the symmetric simple exclusion process.

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