Multiple time-scale approach for a system of Brownian particles in a non-uniform temperature eld

The Smoluchowsky equation for a system of interacting Brownian particles in a temperature gradient is derived from the Kramers equation by means of a multiple time-scale method. The interparticle interactions are assumed to be represented by a mean-eld description. We present numerical results that compare well with the theoretical prediction together with an extensive dis- cussion on the prescription of the Langevin equation in overdamped systems.