The present study extends the correspondence principle of Martinez et al. that establishes a link between nonlinear Fokker–Planck equations (NLFPEs) and the variational principle approach of the theory of canonical ensembles. By virtue of the extended correspondence principle we reobtain...

In correspondence to conventional thermostatistics we formulate an H-theorem showing that transients solutions of nonlinear Fokker–Planck equations related to generalized thermostatistics converge to stationary probability densities. The H-theorem is applied to relaxation processes of...

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...