LAUSR

Anomalous-diffusion phenomena are very common in nature and may be suitably described by means of nonlinear Fokker-Planck equations, characterized by specific types of nonlinear diffusion contributions. The most explored situations in the literature consist in nonlinear diffusion contributions written as a power of the probability; these are directly associated with nonextensive statistical mechanics. In this work, we investigate two special limits of such a diffusion contribution, namely, the exponential and logarithmic ones, corresponding, respectively, to superdiffusive and subdiffusive regimes. An H-theorem is proven, relating these Fokker-Planck equations to entropic forms; moreover, the stationary states of these equations are shown to coincide with the equilibrium states, obtained by extremization of the associated entropic forms. Equilibrium distributions are computed in particular cases, being mostly characterized by long tails in the exponential case, whereas compact-support distributions always appear in the logarithmic one. The present results enlarge the applicability of nonlinear Fokker-Planck equations to a wider range of anomalous-diffusion phenomena, particularly those in special limits of super- and subdiffusion regimes.