8 pages, 2 figures.-- PACS numbers: 05.45.-a, 05.10.Gg.-- arXiv pre-print: http://arxiv.org/abs/cond-mat/0610069.-- Final full-text version of the paper available at: http://dx.doi.org/10.1103/PhysRevE.75.021101.The Smoluchowski 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-field description.
We present numerical results that compare well with the theoretical prediction together with an extensive discussion on the prescription of the Langevin equation in overdamped systems.C.L. acknowledges financial support from MEC (Spain) and FEDER through project CONOCE2 (FIS2004-00953) and from the bilateral project Spain-Italy HI2004-0144. He also acknowledges a Ramón y Cajal research fellow of the Spanish MEC. U.M.B.M. acknowledges a grant COFIN-MIUR 2005, 2005027808
