Quasi-power law ensembles

TL;DR

This paper explores the origins and implications of quasi-power law ensembles modeled by Tsallis distributions, highlighting their connection to nonextensive entropy, different parameters, and their ability to describe complex data behaviors.

Contribution

It demonstrates the relationship between different nonextensive parameters, derives Tsallis distributions from Shannon entropy under specific constraints, and explains their applicability to log-oscillating data.

Findings

Nonextensive parameters from different sources are related by q1 + q2 = 2.

Tsallis distributions can be derived from Shannon entropy with constraints.

They can model log-oscillations in multiparticle data.

Abstract

Quasi-power law ensembles are discussed from the perspective of nonextensive Tsallis distributions characterized by a nonextensive parameter $q$. A number of possible sources of such distributions are presented in more detail. It is further demonstrated that data suggest that nonextensive parameters deduced from Tsallis distributions functions $f\left(p_T\right)$, $q_1$, and from multiplicity distributions (connected with Tsallis entropy), $q_2$, are not identical and that they are connected via $q_1 + q_2 = 2$. It is also shown that Tsallis distributions can be obtained directly from Shannon information entropy, provided some special constraints are imposed. They are connected with the type of dynamical processes under consideration (additive or multiplicative). Finally, it is shown how a Tsallis distribution can accommodate the log-oscillating behavior apparently seen in some multiparticle data.