Nonextensive statistics: theoretical, experimental and computational evidences and connections

TLDR

Nonextensive statistics generalizes Boltzmann–Gibbs thermodynamics to nonextensive systems, a concept introduced in 1988 from multifractal geometry and studied extensively over the past decade. The authors aim to extend the validity of standard thermodynamics to anomalous systems by presenting the formalism and reviewing its theoretical, experimental, and computational evidence. They describe the formalism and compile current theoretical, experimental, and computational evidence, outlining future research directions. The review highlights existing evidence and connections, and identifies open questions that could clarify the foundations of statistical mechanics and its thermodynamic implications.

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 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.