Multivariate nonlinear Fokker–Planck equations and generalized thermostatistics

Multivariate nonlinear Fokker–Planck equations are derived which are solved by equilibrium distributions of generalized thermostatistics. The multivariate Fokker–Planck equations proposed by Kaniadakis and by Borland et al. are re-obtained as special cases. Furthermore, a Kramers equation is derived for particles obeying the nonextensive thermostatistics proposed by Tsallis.