A probabilistic mechanism hidden behind the universal power law for dielectric relaxation: general relaxation equation

Abstract

A new model for the explanation of the universal dielectric response law is proposed. It differs significantly from all previous work on the subject. The presented model is based on the assumption that individual dipoles and their environment do not remain independent during the process of relaxation. Therefore the time theta i needed for the regression to equilibrium of polarization fluctuations is a random variable that depends for each relaxing dipole on two other random variables: the waiting time eta i and the dissipation rate beta i. As a consequence the author derives a general relaxation equation that gives the universal dielectric response in the power-law form (as a special case, the stretched exponential form is obtained).