  A nonlinear Fokker-Planck equation is obtained in the continuous limit of a
one-dimensional lattice with an energy landscape of wells and barriers.
Interaction is possible among particles in the same energy well. A parameter
$\gamma$, related to the barrier's heights, is introduced. Its value is
determinant for the functional dependence of the mobility and diffusion
coefficient on particle concentration, but has no influence on the equilibrium
solution. A relation between the mean field potential and the microscopic
interaction energy is derived. The results are illustrated with classical
particles with interactions that reproduce fermion and boson statistics.
