We present a unified perspective on the hydrodynamic limits of three interacting particle systems in contact with slow boundary reservoirs: the Simple Symmetric Exclusion Process (SSEP), the Porous Medium Model (PMM), and the Symmetric Zero-Range Process (ZR).

Although these systems share the same type of boundary dynamics — particle creation and annihilation at rates of order $N^{-\theta}$ — their bulk dynamics differ substantially: linear exclusion, constrained exclusion with nonlinear mobility, and unbounded occupancy with nonlinear jump rates.

Under diffusive scaling, the empirical density evolves according to a parabolic equation whose form depends on the microscopic interaction. We show how the strength of the reservoirs determines a phase transition in the macroscopic boundary conditions: Dirichlet for $\theta < 1$, Robin for $\theta = 1$, and Neumann for $\theta > 1$.

This comparison highlights how microscopic mechanisms shape macroscopic diffusion, while revealing a universal boundary transition driven by slow reservoirs.