J. R. Campanha | Searcharxiv

arXiv2000

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.

cond-mat.stat-mech↗

arXiv2000

A Generalized Smoluchowsky Equation: The Hydrodynamical and Thermodynamical Picture of Brownian Motion

We present a systematic expansion of Kramers equation in the high friction limit. The latter is expanded within an operator continued fraction scheme. The relevant operators include both temporal and spatial derivatives and a covariant derivate or gauge like operator associated to the potential energy. Trivially, the first order term yields the Smoluchowsky equation. The second order term is readily obtained, known as the corrected Smoluchowsky equation. Further terms are computed in compact and straightforward fashion. As an application, the nonequilibrium thermodynamics and hydrodynamical schemes for the one dimensional Brownian motion is presented.

cond-mat.stat-mech↗