Chapman–Enskog derivation of the generalized Smoluchowski equation

Pierre-Henri Chavanis, Philippe Laurençot and Mohammed Lemou

Physica A: Statistical Mechanics and its Applications, 2004, vol. 341, issue C, 145-164

Abstract: We use the Chapman–Enskog method to derive the Smoluchowski equation from the Kramers equation in a high friction limit. We consider two main extensions of this problem: we take into account a uniform rotation of the background medium and we consider a generalized class of Kramers equations associated with generalized free energy functionals. We mention applications of these results to systems with long-range interactions (self-gravitating systems, 2D vortices, bacterial populations, etc.). In that case, the Smoluchowski equation is non-local. In the limit of short-range interactions, it reduces to a generalized form of the Cahn–Hilliard equation. These equations are associated with an effective generalized thermodynamical formalism.

Keywords: Kinetic theory; Generalized thermodynamics; Generalized Fokker–Planck equations (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:341:y:2004:i:c:p:145-164

DOI: 10.1016/j.physa.2004.04.102

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