The thermohydrodynamical picture of a charged Brownian particle

TL;DR

This paper develops a thermohydrodynamical framework for a charged Brownian particle in non-uniform temperature environments, analyzing local equilibrium validity and deriving gradient corrections and fundamental equations for particle density.

Contribution

It introduces a novel thermohydrodynamical approach to charged Brownian motion, including new results on local equilibrium and nonlinear gradient corrections.

Findings

Validity range of local equilibrium approach analyzed

Gradient corrections to Smoluchowski equation derived

Applications to linear and nonlinear regimes presented

Abstract

We study a charged Brownian gas with a non uniform bath temperature, and present a thermohydrodynamical picture. Expansion on the collision time probes the validity of the local equilibrium approach and the relevant thermodynamical variables. For the linear regime we present several applications (including some novel results). For the lowest nonlinear expansion and uniform bath temperature we compute the gradient corrections to the local equilibrium approach and the fundamental (Smoluchowsky) equation for the nonequilibrium particle density.