Entropic origin of dielectric relaxation universalities in heterogeneous materials (polymers, glasses, aerogel catalysts)

We have derived a universal relaxation function for heterogeneous materials using the maximum entropy principle for nonextensive systems. The power law exponents of the relaxation function are simply related to a global fractal parameter and for large time to the entropy nonextensivity parameter q. For intermediate times the relaxation follows a stretched exponential behavior. The asymptotic power law behaviors both in the time and the frequency domains coincide with those of the Weron generalized dielectric function derived in the stochastic theory from an extension of the Levy central limit theorem. These results are in full agreement with the Jonscher universality principle and find application in the characterization of the dielectric properties of aerogels catalytic supports as well as in the problem of the relation between morphology and dielectric properties of polymer composites.