"Lie symmetries of the nonlinear Fokker-Planck equation based on weighted Tsallis entropy"

Pripoae, Cristina-Liliana; Hirica, Iulia-Elena; PRIPOAE, GABRIEL- TEODOR; Preda, Vasile

doi:10.37193/cjm.2022.03.07

Cited by 6 publications

(8 citation statements)

References 33 publications

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“…In this section, we recall some notions and results from [49,50,91,102], concerning the nonlinear Fokker-Planck equation (NFPE), including important examples of entropies, needed for our next discussion in Section 3.…”

Section: Preliminary Notions and Resultsmentioning

confidence: 99%

“…In our papers [50,91], we generalized these results, for the case of weighted STM, Tsallis and Kaniadakis entropies, respectively. In the final classification of symmetries, the Lie algebras differentiate by means of six "exceptional" values of the Tsallis parameter q and by two "exceptional" values of the Kaniadakis parameter k.…”

Section: Will This Approach Work For Entropy Models As Well ?mentioning

confidence: 86%

“…where δ = k, for (i); δ = −k, for (ii); δ = k − 1 2 , for (iii); δ = −k − 1 2 , for (iv). In [91], we remarked that the previous Lie symmetries point out "exceptional" cases which reveal that the respective Tsallis entropies differ fundamentally from the resting cases. We conjectured that this entropies correspond to some optimal situation, the "maximal symmetry" being associated to the "maximal stability" (in agreement with [26,117]).…”

Section: The Sinkala's Classification and The Six "Exceptional" Value...mentioning

confidence: 94%

“…In Section 2, we recall some of our recent results ( [50,91]) concerning the Lie symmetries associated to the nonlinear Fokker-Plank equations derived from weighted Kaniadakis or Tsallis entropies. Six 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.…”

Section: Our Contributionmentioning

confidence: 99%

“…The corresponding Lie symmetries were determined in [102] (and were recovered in [50,91], from our similar studies, based on the weighted Tsallis and weighted Kaniadakis entropies). The only such entropies which produce Lie symmetries, apart the generic ones…”

Section: The Sinkala's Classification and The Six "Exceptional" Value...mentioning

confidence: 99%

See 4 more Smart Citations

Entropy- A Tale of Ice and Fire

Hirica¹,

Pripoae²,

Pripoae³

et al. 2023

Annals of West University of Timisoara - Mathematics and Computer Science

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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.

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Section: Preliminary Notions and Resultsmentioning

confidence: 99%

Section: Will This Approach Work For Entropy Models As Well ?mentioning

confidence: 86%

Section: The Sinkala's Classification and The Six "Exceptional" Value...mentioning

confidence: 94%

Section: Our Contributionmentioning

confidence: 99%

Section: The Sinkala's Classification and The Six "Exceptional" Value...mentioning

confidence: 99%

See 3 more Smart Citations

Entropy- A Tale of Ice and Fire

Hirica¹,

Pripoae²,

Pripoae³

et al. 2023

Annals of West University of Timisoara - Mathematics and Computer Science

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Some Properties of Fractal Tsallis Entropy

Preda

Sfetcu

2023

Fractal Fract

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We introduce fractal Tsallis entropy and show that it satisfies Shannon–Khinchin axioms. Analogously to Tsallis divergence (or Tsallis relative entropy, according to some authors), fractal Tsallis divergence is defined and some properties of it are studied. Within this framework, Lesche stability is verified and an example concerning the microcanonical ensemble is given. We generalize the LMC complexity measure (LMC is Lopez-Ruiz, Mancini and Calbert), apply it to a two-level system and define the statistical complexity by using the Euclidean and Wootters’ distance measures in order to analyze it for two-level systems.

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Lie Symmetries of the Nonlinear Fokker-Planck Equation Based on Weighted Kaniadakis Entropy

Hirica

Pripoae

et al. 2022

Mathematics

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The paper studies the Lie symmetries of the nonlinear Fokker–Planck equation in one dimension, which are associated to the weighted Kaniadakis entropy. In particular, the Lie symmetries of the nonlinear diffusive equation, associated to the weighted Kaniadakis entropy, are found. The MaxEnt problem associated to the weighted Kaniadakis entropy is given a complete solution, together with the thermodynamic relations which extend the known ones from the non-weighted case. Several different, but related, arguments point out a subtle dichotomous behavior of the Kaniadakis constant k, distinguishing between the cases k∈(−1,1) and k=±1. By comparison, the Lie symmetries of the NFPEs based on Tsallis q-entropies point out six “exceptional” cases, for: q=12, q=32, q=43, q=73, q=2 and q=3.

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"Lie symmetries of the nonlinear Fokker-Planck equation based on weighted Tsallis entropy"

Cited by 6 publications

References 33 publications

Entropy- A Tale of Ice and Fire

Entropy- A Tale of Ice and Fire

Some Properties of Fractal Tsallis Entropy

Lie Symmetries of the Nonlinear Fokker-Planck Equation Based on Weighted Kaniadakis Entropy

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