Next Article in Journal
The Homological Nature of Entropy
Next Article in Special Issue
Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation
Previous Article in Journal
Quantum Data Locking for Secure Communication against an Eavesdropper with Time-Limited Storage
Previous Article in Special Issue
On the κ-Deformed Cyclic Functions and the Generalized Fourier Series in the Framework of the κ-Algebra

Generalized Stochastic Fokker-Planck Equations

Laboratoire de Physique Théorique, Université Paul Sabatier, 118 route de Narbonne 31062 Toulouse, France
Academic Editor: Giorgio Kaniadakis
Entropy 2015, 17(5), 3205-3252;
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)
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
MDPI and ACS Style

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

AMA Style

Chavanis P-H. Generalized Stochastic Fokker-Planck Equations. Entropy. 2015; 17(5):3205-3252.

Chicago/Turabian Style

Chavanis, Pierre-Henri. 2015. "Generalized Stochastic Fokker-Planck Equations" Entropy 17, no. 5: 3205-3252.

Find Other Styles

Article Access Map by Country/Region

Only visits after 24 November 2015 are recorded.
Back to TopTop