Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics

We study the hydrodynamic and hydrostatic limits of one-dimensional open symmetric inclusion process with slow boundary. Depending on value parameter tuning interaction rate bulk system boundary, we obtain a linear heat equation either Dirichlet, Robin or Neumann boundary conditions as equation. In our approach, combine duality first-second class particle techniques to reduce scaling limit limiting behavior single, non-interacting, particle.