Non-extensive statistical mechanics and generalized Fokker-Planck equation

A non-linear, generalized Fokker-Planck (GFP) equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by Tsallis in his generalization of Statistical Mechanics. In the case of a constant or linearly varying drift, the time dependent solutions of the GFP equation are seen to obey a suitable form of the celebrated H-theorem. The temporal changes of Tsallisʹ entropies are seen to be given in terms of the Fisherʹs information measure. Particular time-dependent solutions of the GFP equation of the maximum (Tsallisʹ) entropy form are obtained.