English

Equilibrium of a Brownian particle with coordinate dependent diffusivity and damping: Generalized Boltzmann distribution

Statistical Mechanics 2018-10-01 v5

Abstract

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.

Keywords

Cite

@article{arxiv.1708.06132,
  title  = {Equilibrium of a Brownian particle with coordinate dependent diffusivity and damping: Generalized Boltzmann distribution},
  author = {A. Bhattacharyay},
  journal= {arXiv preprint arXiv:1708.06132},
  year   = {2018}
}

Comments

11 pages, 1 figure