Application of the Widom insertion formula to transition rates in a lattice

DI MURO, M. A.; HOYUELOS, M.

Physical Review E

APS

Año: 2021 vol. 104

2470-0045

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.