Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions. It emphasizes principles and concepts of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution). The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.

First textbook that deals with the nonlinear Fokker-Planck equations

Inhalt
Fundamentals.- Strongly Nonlinear Fokker-Planck Equations.- Free Energy Fokker-Planck Equations.- Free Energy Fokker-Planck Equations with Boltzmann Statistics.- Entropy Fokker-Planck Equations.- General Nonlinear Fokker-Planck Equations.- Epilogue.