Nonextensive statistics: Theoretical, experimental and computational evidences and connections

TL;DR

This paper reviews the development and current status of nonextensive statistical mechanics, discussing its theoretical foundations, experimental and computational evidence, and future perspectives in extending thermodynamics beyond Boltzmann-Gibbs framework.

Contribution

It provides a comprehensive overview of nonextensive statistics, highlighting recent advances, evidences, and open questions that challenge and extend traditional thermodynamics.

Findings

The formalism of nonextensive statistics is well-developed and supported by various evidences.

Experimental and computational results increasingly confirm the relevance of nonextensive approaches.

Open questions remain about the foundational implications and future applications of nonextensive thermodynamics.

Abstract

The domain of validity of standard thermodynamics and Boltzmann-Gibbs statistical mechanics is discussed and then formally enlarged in order to hopefully cover a variety of anomalous systems. The generalization concerns {\it nonextensive} systems, where nonextensivity is understood in the thermodynamical sense. This generalization was first proposed in 1988 inspired by the probabilistic description of multifractal geometries, and has been intensively studied during this decade. In the present effort, after introducing some historical background, we briefly describe the formalism, and then exhibit the present status in what concerns theoretical, experimental and computational evidences and connections, as well as some perspectives for the future. In addition to these, here and there we point out various (possibly) relevant questions, whose answer would certainly clarify our current understanding of the foundations of statistical mechanics and its thermodynamical implications