Nonlinear Fokker–Planck equations whose stationary solutions make entropy-like functionals stationary

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 results of Kaniadakis and Quarati for Bose and Fermi systems and find relations similar to those derived by Plastino and Plastino and recently by Borland concerning the entropy of nonextensive thermostatistics introduced in physics by Tsallis. Moreover, we propose NLFPEs related to the Renyi entropy and to the entropy proposed by Sharma and Mittal. The latter comprises Tsallis’ entropy and the Renyi entropy.