Relaxation in heterogeneous systems: A rare events dominated phenomenon

We have derived a general two-power-law 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 α 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 Lévy central limit theorem. These results are in full agreement with the Jonscher universality principle and trace the origin of the large t power law universality (with system dependent exponent α and q) to the scaling behavior of the extreme value distribution function of the effective macroscopic waiting time and the fluctuation of the number of relaxing entities.