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

Author

Listed:
  • Iulia-Elena Hirica

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania)

  • Cristina-Liliana Pripoae

    (Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana 6, RO-010374 Bucharest, Romania)

  • Gabriel-Teodor Pripoae

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania)

  • Vasile Preda

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania
    “Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of Romanian Academy, 2. Calea 13 Septembrie, Nr. 13, Sect. 5, RO-050711 Bucharest, Romania
    “Costin C. Kiritescu” National Institute of Economic Research of Romanian Academy, 3. Calea 13 Septembrie, Nr. 13, Sect. 5, RO-050711 Bucharest, Romania)

Abstract

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 = 1 2 , q = 3 2 , q = 4 3 , q = 7 3 , q = 2 and q = 3 .

Suggested Citation

  • Iulia-Elena Hirica & Cristina-Liliana Pripoae & Gabriel-Teodor Pripoae & Vasile Preda, 2022. "Lie Symmetries of the Nonlinear Fokker-Planck Equation Based on Weighted Kaniadakis Entropy," Mathematics, MDPI, vol. 10(15), pages 1-22, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2776-:d:880663
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    References listed on IDEAS

    as
    1. T. Wada & A. M. Scarfone, 2009. "Asymptotic solutions of a nonlinear diffusive equation in the framework of κ-generalized statistical mechanics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 65-71, July.
    2. Jia Zheng, 2020. "Lie Symmetry Analysis and Invariant Solutions of a Nonlinear Fokker-Planck Equation Describing Cell Population Growth," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-7, January.
    3. Ebrahimi, Nader & Soofi, Ehsan S. & Soyer, Refik, 2008. "Multivariate maximum entropy identification, transformation, and dependence," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1217-1231, July.
    4. An, Ing & Chen, Shi & Guo, Han-ying, 1984. "Search for the symmetry of the Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(3), pages 520-528.
    5. Jizba, Petr & Korbel, Jan, 2016. "On q-non-extensive statistics with non-Tsallisian entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 808-827.
    6. Marius Giuclea & Costin-Ciprian Popescu, 2022. "On Geometric Mean and Cumulative Residual Entropy for Two Random Variables with Lindley Type Distribution," Mathematics, MDPI, vol. 10(9), pages 1-10, April.
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    Cited by:

    1. Răzvan-Cornel Sfetcu & Vasile Preda, 2024. "Order Properties Concerning Tsallis Residual Entropy," Mathematics, MDPI, vol. 12(3), pages 1-16, January.
    2. Răzvan-Cornel Sfetcu & Vasile Preda, 2023. "Fractal Divergences of Generalized Jacobi Polynomials," Mathematics, MDPI, vol. 11(16), pages 1-12, August.
    3. Cristina-Liliana Pripoae & Iulia-Elena Hirica & Gabriel-Teodor Pripoae & Vasile Preda, 2022. "Fisher-like Metrics Associated with ϕ -Deformed (Naudts) Entropies," Mathematics, MDPI, vol. 10(22), pages 1-26, November.

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