Local evolution rules and the diffusion equation

A partial differential equation describing the diffusion of a set of interacting particles on a lattice is obtained using the so-called local evolution rules approach. This equation is derived after truncating a hierarchy of partial differential equations using a mean-field (m, n) closure. Both, the partial differential equations and the diffusion coefficients, are derived in a variety of cases. The description of the noninteracting set of particles is obtained always as a limiting case. The results are compared to those previously obtained by other method.