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The Nonadditive Entropy Sq and Its Applications in Physics and Elsewhere: Some Remarks

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Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil
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Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
Entropy 2011, 13(10), 1765-1804; https://doi.org/10.3390/e13101765
Received: 15 August 2011 / Revised: 11 September 2011 / Accepted: 19 September 2011 / Published: 28 September 2011
(This article belongs to the Special Issue Tsallis Entropy)
The nonadditive entropy Sq has been introduced in 1988 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 Sq 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. View Full-Text
Keywords: nonadditive entropy; nonextensive statistical mechanics; complex systems nonadditive entropy; nonextensive statistical mechanics; complex systems
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Tsallis, C. The Nonadditive Entropy Sq and Its Applications in Physics and Elsewhere: Some Remarks. Entropy 2011, 13, 1765-1804.

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