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. Con sequently, 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. (C) 1998 Elsevier Science B,V. All rights reserved.