The $q$-canonical ensemble as a consequence of Bayesian superstatistics

Abstract

In this work it is shown that the main ensemble of Tsallis nonextensive statistics, namely the χ 2 -superstatistics, can be obtained as a noninformative prior distribution that is singled out by the mathematical structure of superstatistics itself. There are no assumptions involved about the physics of the systems of interest, or regarding their complexity or range of interactions, which supports the thesis that the success of the χ 2 -superstatistics is information-theoretical in its origin, and explainable in terms of Jaynes' original maximum entropy principle.