Derivation and validation of mesoscopic theories for diffusion of interacting molecules

A mesoscopic theory for diffusion of molecules interacting with a long-rang e potential is derived for Arrhenius microscopic dynamics. Gradient Monte C arlo simulations are presented on a one-dimensional lattice to assess the v alidity of the mesoscopic theory. Results are compared for Metropolis and A rrhenius microscopic dynamics. Non-Fickian behavior is demonstrated and it is shown that microscopic dynamics dictate the steady-state concentration p rofiles.