<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In 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.</p>
<p>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.</p>
</abstract>

In 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.

Entropy- A Tale of Ice and Fire

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

(Review of some exceptional Tsallis indexes)

In this review paper, we recall, in a unifying manner, our recent results concerning the Lie symmetries of nonlinear Fokker-Plank equations, associated to the...

Entropy- A Tale of Ice and Fire

Published Online: May 03, 2023

Page range: 1 - 20

DOI: https://doi.org/10.2478/awutm-2023-0002

Keywords
Tsallis entropy, Fokker-Plank equations, special values of Tsallis parameters

© 2023 Iulia-Elena Hirica et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Entropy- A Tale of Ice and Fire

Published Online: May 03, 2023

Page range: 1 - 20

DOI: https://doi.org/10.2478/awutm-2023-0002

KeywordsTsallis entropy, Fokker-Plank equations, special values of Tsallis parameters

© 2023 Iulia-Elena Hirica et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Tsallis entropy, Fokker-Plank equations, special values of Tsallis parameters