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It is pointed out that the generalized statistical mechanics introduced by Tsallis [J. Stat. Phys. 52, 479 (1988)] provides a natural frame for developing a thermodynamical formalism of anomalous diffusion. Within such a frame, we calculate the mean square displacement as a function of time and generalize the Einstein relation of diffusivity and temperature for random walks of the L\'evy-flight type.
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Zanette et al. (1995) studied this question.
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