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 radian to the energy stored in the system, in the corresponding frequency range. For almost two decades, the above energy criterion has been supposed to imply the existence of similar microscopic properties which determine the observed power-law exponent. Here, a rigorous formulation of the energy-criterion argument is proposed in the frame of a new probabilistic approach to derive the Havriliak-Negami (HN) and Kohlraush-Williams-Watts (KWW) responses. In this approach the commonly observed macroscopic laws are related to the microscopic scenario of relaxation, and the energy-criterion interpretation is applied to the physical basis of the relation. The presented considerations reinforce the physical significance of the empirically found forms of relaxation, and open a new line of analysis of relaxation phenomena.