Nonlinear Fokker–Planck equations and generalized entropies

We consider maximum entropy solutions to Nonlinear Fokker–Planck equations within general thermostatistical formalisms. We show that the family of generalized nonextensive entropies introduced by Tsallis is the only one that has an associated family of nonlinear Fokker–Planck equations endowed with time-dependent MaxEnt solutions of a generalized Gaussian type. Consequently, the natural association that arises between Tsallis’ thermostatistical formalism and special families of nonlinear Fokker–Planck equations is NOT a universal feature of general thermostatistical formalisms, but a particular feature of the Tsallis’ one.