Nonadditive entropy and nonextensive statistical mechanics - Some central concepts and recent applications

TL;DR

This paper reviews the core ideas of nonextensive statistical mechanics based on nonadditive entropy, exploring its theoretical foundations and recent applications such as generalized CLT and systems at the edge of chaos.

Contribution

It provides a concise overview of nonextensive entropy concepts and discusses recent developments in their applications to complex systems.

Findings

Possible realizations of the q-generalized Central Limit Theorem

Applications to systems at the edge of chaos

Analysis of quasi-stationary states in long-range interacting systems

Abstract

We briefly review central concepts concerning nonextensive statistical mechanics, based on the nonadditive entropy $S_q=k\frac{1-\sum_{i}p_i^q}{q-1} (q \in {\cal R}; S_1=-k\sum_{i}p_i \ln p_i)$. Among others, we focus on possible realizations of the $q$-generalized Central Limit Theorem, including at the edge of chaos of the logistic map, and for quasi-stationary states of many-body long-range-interacting Hamiltonian systems.