A microscopic mechanism for the porous medium equation

The porous medium equation on a d-dimensional torus is obtained as a hydrodynamic scaling limit, with the usual diffusion scaling, of the empirical measures of a sequence of reversible Markov jump processes on approximating periodic lattices. Each process can be viewed as a randomly interacting configuration of sticks (or energies, etc.). The configuration evolves through exchanges of stick portions that occur between nearest neighbours through …