Energy criterion in interacting cluster systems

The high-frequency fractional power law of relaxation, seen in a wide range of materials, yields a constant ratio of the macroscopic energy lost per r adian to the energy stored in the system, in the corresponding frequency ra nge. For almost two decades, the above energy criterion has been supposed t o imply the existence of similar microscopic properties which determine the observed power-law exponent. Here, a rigorous formulation of the energy-cr iterion argument is proposed in the frame of a new probabilistic approach t o derive the Havriliak-Negami (HN) and Kohlraush-Williams-Watts (KWW) respo nses. In this approach the commonly observed macroscopic laws are related t o the microscopic scenario of relaxation, and the energy-criterion interpre tation is applied to the physical basis of the relation. The presented cons iderations reinforce the physical significance of the empirically found for ms of relaxation, and open a new line of analysis of relaxation phenomena.