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Entropy- A Tale of Ice and Fire

Entropy- A Tale of Ice and Fire AbstractIn this review paper, we recall, in a unifying manner, our recent results concerning the Lie symmetries of nonlinear Fokker-Plank equations, associated to the (weighted) Tsallis and Kaniadakis entropies. The special values of the Tsallis parameters, highlighted by the classification of these symmetries, clearly indicate algebraic and geometric invariants which differentiate the Lie algebras involved. We compare these values with the ones previously obtained by several authors, and we try to establish connections between our theoretical families of entropies and specific entropies arising in several applications found in the literature.We focus on the discovered correlations, but we do not neglect dissimilarities, which might provide -in the future-deeper details for an improved extended panorama of the Tsallis entropies. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of West University of Timisoara - Mathematics de Gruyter

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References (137)

Publisher
de Gruyter
Copyright
© 2023 Iulia-Elena Hirica et al., published by Sciendo
ISSN
1841-3307
eISSN
1841-3307
DOI
10.2478/awutm-2023-0002
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this review paper, we recall, in a unifying manner, our recent results concerning the Lie symmetries of nonlinear Fokker-Plank equations, associated to the (weighted) Tsallis and Kaniadakis entropies. The special values of the Tsallis parameters, highlighted by the classification of these symmetries, clearly indicate algebraic and geometric invariants which differentiate the Lie algebras involved. We compare these values with the ones previously obtained by several authors, and we try to establish connections between our theoretical families of entropies and specific entropies arising in several applications found in the literature.We focus on the discovered correlations, but we do not neglect dissimilarities, which might provide -in the future-deeper details for an improved extended panorama of the Tsallis entropies.

Journal

Annals of West University of Timisoara - Mathematicsde Gruyter

Published: Jun 1, 2023

Keywords: Tsallis entropy; Fokker-Plank equations; special values of Tsallis parameters; 35Q84; 22E70; 35Q82; 70G65; 82C31; 94A17

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