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Entropy 2015, 17(5), 3205-3252; doi:10.3390/e17053205

Generalized Stochastic Fokker-Planck Equations

Laboratoire de Physique Théorique, Université Paul Sabatier, 118 route de Narbonne 31062 Toulouse, France
Academic Editor: Giorgio Kaniadakis
Received: 2 March 2015 / Revised: 23 April 2015 / Accepted: 27 April 2015 / Published: 13 May 2015
(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)
View Full-Text   |   Download PDF [382 KB, uploaded 19 May 2015]

Abstract

We consider a system of Brownian particles with long-range interactions. We go beyond the mean field approximation and take fluctuations into account. We introduce a new class of stochastic Fokker-Planck equations associated with a generalized thermodynamical formalism. Generalized thermodynamics arises in the case of complex systems experiencing small-scale constraints. In the limit of short-range interactions, we obtain a generalized class of stochastic Cahn-Hilliard equations. Our formalism has application for several systems of physical interest including self-gravitating Brownian particles, colloid particles at a fluid interface, superconductors of type II, nucleation, the chemotaxis of bacterial populations, and two-dimensional turbulence. We also introduce a new type of generalized entropy taking into account anomalous diffusion and exclusion or inclusion constraints. View Full-Text
Keywords: nonlinear Fokker-Planck equations; generalized entropies; long-range systems nonlinear Fokker-Planck equations; generalized entropies; long-range systems
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Chavanis, P.-H. Generalized Stochastic Fokker-Planck Equations. Entropy 2015, 17, 3205-3252.

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