Burr, Levy, Tsallis

TL;DR

This paper explores how mathematical tools from Burr, Lévy, and Tsallis provide new insights into non-Debye decay and relaxation universality, linking finite characteristic times to q-expectations and comparing with existing probabilistic theories.

Contribution

It demonstrates the application of Burr, Lévy, and Tsallis concepts to analyze non-Debye relaxation and introduces a q-expectation framework for characteristic times.

Findings

Finite characteristic time expressed via q-expectation.

Enhanced understanding of stochastic properties of Tsallis entropy.

Comparison with Weron et al. theory clarifies underlying relaxation mechanisms.

Abstract

The purpose of this short paper dedicated to the 60th anniversary of Prof.Constantin Tsallis is to show how the use of mathematical tools and physical concepts introduced by Burr, L\.{e}vy and Tsallis open a new line of analysis of the old problem of non-Debye decay and universality of relaxation. We also show how a finite characteristic time scale can be expressed in terms of a $q$-expectation using the concept of $q$- escort probability.The comparison with the Weron et al. probabilistic theory of relaxation leads to a better understanding of the stochastic properties underlying the Tsallis entropy concept.