  We consider diffusion of particles on a lattice in the so-called dynamical
mean-field regime (memory effects are neglected). Interactions are local, that
is, only among particles at the same lattice site. It is shown that a
statistical mechanics analysis that combines detailed balance and Widom's
insertion formula allows for the derivation of an expression for transition
rates in terms of the excess chemical potential. The rates reproduce the known
dependence of self-diffusivity as the inverse of the thermodynamic factor.
Soft-core interactions and general forms of the excess chemical potential
(linear, quadratic, and cubic with the density) are considered.
