Nonlinear mean-field Fokker–Planck equations and their applications in physics, astrophysics and biology

We discuss a general class of nonlinear mean-field Fokker–Planck equations [P.-H. Chavanis, Phys. Rev. E 68 (2003) 036108] and show their applications in different domains of physics, astrophysics and biology. These equations are associated with generalized entropic functionals and non-Boltzmannian distributions (Fermi–Dirac, Bose–Einstein, Tsallis, …). They furthermore involve an arbitrary binary potential of interaction. We emphasize analogies between different topics (two-dimensional turbulence, self-gravitating systems, Debye–Hückel theory of electrolytes, porous media, chemotaxis of bacterial populations, Bose–Einstein condensation, BMF model, Cahn–Hilliard equations, …) which were previously disconnected. All these examples (and probably many others) are particular cases of this general class of nonlinear mean-field Fokker–Planck equations. To cite this article: P.-H. Chavanis, C. R. Physique 7 (2006).