Nonextensive statistical mechanics: A brief review of its present status

TL;DR

This paper reviews the current state of nonextensive statistical mechanics, discussing its core equations, recent applications across sciences, and methods to determine the entropic index q from microscopic dynamics in specific physical systems.

Contribution

It provides a concise overview of the formalism, recent applications, and methods to derive the entropic index q for key classes of physical systems.

Findings

Overview of the central equations of nonextensive statistical mechanics

Recent applications in physics and other sciences

Methods to determine the entropic index q from microscopic dynamics

Abstract

We briefly review the present status of nonextensive statistical mechanics. We focus on (i) the central equations of the formalism, (ii) the most recent applications in physics and other sciences, (iii) the {\it a priori} determination (from microscopic dynamics) of the entropic index $q$ for two important classes of physical systems, namely low-dimensional maps (both dissipative and conservative) and long-range interacting many-body hamiltonian classical systems.