2017/08/21 by A. Bhattacharyay, Bhattacharyay, A.
Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Material Dynamics and Properties #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1708.06132
11 pages, 1 figure
openalex publication_date 2017/08/21 · arxiv created 2018/09/28 · arxiv updated 2018/10/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Fick's law for coordinate dependent diffusivity is derived. Corresponding diffusion current in the presence of coordinate dependent diffusivity is consistent with the form as given by Kramers-Moyal expansion. We have obtained the equilibrium solution of the corresponding Smoluchowski equation. The equilibrium distribution is a generalization of the Boltzmann distribution. This generalized Boltzmann distribution involves an effective potential which is a function of coordinate dependent diffusivity. We discuss various implications of the existence of this generalized Boltzmann distribution for equilibrium of systems with coordinate dependent diffusivity and damping.