Microscopic Dynamics Of Nonlinear Fokker-Planck Equations

We propose an approach to describe the effective microscopic dynamics of (power-law) nonlinear Fokker-Planck equations. Our formalism is based on a nonextensive generalization of the Wiener process. This allows us to obtain, in addition to significant physical insights, several analytical results with great simplicity. Indeed, we obtain analytical solutions for a nonextensive version of the Brownian free-particle and Ornstein-Uhlenbeck processes, and we explain anomalous diffusive behaviors in terms of memory effects in a nonextensive generalization of Gaussian white noise. Finally, we apply the developed formalism to model thermal noise in electric circuits.