Fick and Fokker–Planck diffusion law in inhomogeneous media
We discuss particle diffusion in a spatially inhomogeneous medium. From the micro-
scopic viewpoint we consider independent particles randomly evolving on a lattice. We
show that the reversibility condition has a discrete geometric interpretation in terms of
weights associated to un–oriented edges and vertices. We consider the hydrodynamic
diffusive scaling that gives, as a macroscopic evolution equation, the Fokker–Planck equa-
tion corresponding to the evolution of the probability distribution of a reversible spatially