Application of the Widom insertion formula to transition rates in a lattice
Statistical Mechanics
2021-12-03 v3
Abstract
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.
Keywords
Cite
@article{arxiv.2107.06765,
title = {Application of the Widom insertion formula to transition rates in a lattice},
author = {Matías A. Di Muro and Miguel Hoyuelos},
journal= {arXiv preprint arXiv:2107.06765},
year = {2021}
}