Porous Medium Model: An Algebraic Perspective and the Fick’s Law

In this work, we study the porous medium model (PMM), an interacting particle system with nearest neighbor interactions of particles under some constraints. First, we consider the discrete space { 1, …, n- 1 } with additional Glauber dynamics acting respectively on sites 0 and n. We assume the hydrodynamic limit (proved in a companion paper [4]) and we prove that the Fick’s law holds. Moreover, we review how to construct a self-duality relation starting from the reversible measure of the process. Following this method, we show a self-duality result for the process without reservoirs, which is found inspired by its description via the Lie algebra su(2 ).