The nonadditive entropy \(S_q\) and its applications in physics and elsewhere: some remarks
type: Item
instance of: scholarly article
title: The nonadditive entropy \(S_q\) and its applications in physics and elsewhere: some remarks
zbMATH Open document ID: 1301.82004
author: C. Tsallis
published in: Entropy
publication date: 2014-08-26T00:00:00Z
review text: Summary: The nonadditive entropy \(S_q\) has been introduced in 1988 [the author, J. Stat. Phys. 52, No. 1--2, 479--487 (1988; Zbl 1082.82501)] focusing on a generalization of Boltzmann-Gibbs (BG) statistical mechanics. The aim was to cover a (possibly wide) class of systems among those very many which violate hypothesis such as ergodicity, under which the BG theory is expected to be valid. It is now known that \(S_q\) has a large applicability; more specifically speaking, even outside Hamiltonian systems and their thermodynamical approach. In the present paper we review and comment some relevant aspects of this entropy, namely (i) Additivity versus extensivity; (ii) Probability distributions that constitute attractors in the sense of Central Limit Theorems; (iii) The analysis of paradigmatic low-dimensional nonlinear dynamical systems near the edge of chaos; and (iv) The analysis of paradigmatic long-range-interacting many-body classical Hamiltonian systems. Finally, we exhibit recent as well as typical predictions, verifications and applications of these concepts in natural, artificial, and social systems, as shown through theoretical, experimental, observational and computational results.
Mathematics Subject Classification ID: 82B03
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 6334276
zbMATH Keywords: nonadditive entropy
zbMATH Keywords: nonextensive statistical mechanics
zbMATH Keywords: complex systems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/e13101765
OpenAlex ID: W2017963899
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DOI: 10.3390/E13101765
description: scientific article; zbMATH DE number 6334276