Abstract
Using the memory conception developed in the framework of the Mori-Zwanzig formalism, the kinetic equations for relaxation functions that correspond to the previously suggested empirical functions (Cole-Davidson and Havriliak-Negami) are derived. The obtained kinetic equations contain differential operators of non-integer order and have clear physical meaning and interpretation. The derivation of the memory function corresponding to the Havriliak-Negami relaxation law in the frame of Mori-Zwanzig formalism is given. A physical interpretation of the power-law exponents involved in the Havriliak-Negami empirical expression is provided too.
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Khamzin, A.A., Nigmatullin, R.R. & Popov, I.I. Justification of the empirical laws of the anomalous dielectric relaxation in the framework of the memory function formalism. fcaa 17, 247–258 (2014). https://doi.org/10.2478/s13540-014-0165-5
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DOI: https://doi.org/10.2478/s13540-014-0165-5