It was pointed out that a generalized statistical mechanics method provided a natural framework for the development of a thermodynamic formalism for anomalous diffusion. Calculations were made of the mean square displacement as a function of time, within such a framework, and the Einstein relationship between diffusivity and temperature was generalized to random walks of the Lévy-flight type. The results revealed a strong formal parallelism between the thermodynamic properties of ordinary diffusion (as treated by means of Boltzmann-Gibbs statistics), and those of anomalous diffusion, with respect to the generalized statistical formulation.

D.H.Zanette, P.A.Alemany: Physical Review Letters, 1995, 75[3], 366-9