The thermohydrodynamical picture of a charged Brownian particle

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.