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

Lopez, C.; Marini B. Marconi, U.
Physical Review E 75, 021101 (2007)

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.