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We have derived the dipolar relaxation function for a cluster model whosevolume distribution was obtained from the generalized maximum Tsallisnonextensive entropy principle. The power law exponents of the relaxationfunction are simply related to a global fractal parameter $\alpha$ and forlarge time to the entropy nonextensivity parameter $q$. For intermediate timesthe relaxation follows a stretched exponential behavior. The asymptotic powerlaw behaviors both in the time and the frequency domains coincide with those ofthe Weron generalized dielectric function derived from an extension of the Levycentral limit theorem. They are in full agreement with the Jonscheruniversality principle. Moreover our model gives a physical interpretation ofthe mathematical parameters of the Weron stochastic theory and opens new pathsto understand the ubiquity of self-similarity and power laws in the relaxationof large classes of materials in terms of their fractal and nonextensiveproperties.Comment: Two figures. Submitted for publicatio

Universal relaxation in nonextensive systems