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arXiv · 1708.06132

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

A. Bhattacharyay
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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.

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A. Bhattacharyay. 2017-08-21. Equilibrium of a Brownian particle with coordinate dependent diffusivity and damping: Generalized Boltzmann distribution. https://arxiv.org/abs/1708.06132

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