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Fisher-like Metrics Associated with ϕ -Deformed (Naudts) Entropies

Author

Listed:
  • Cristina-Liliana Pripoae

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

  • Iulia-Elena Hirica

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 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 defines and studies new semi-Riemannian generalized Fisher metrics and Fisher-like metrics, associated with entropies and divergences. Examples of seven such families are provided, based on exponential PDFs. The particular case when the basic entropy is a ϕ -deformed one, in the sense of Naudts, is investigated in detail, with emphasis on the variation of the emergent scalar curvatures. Moreover, the paper highlights the impact on these geometries determined by the addition of some group logarithms.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4311-:d:976174
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    References listed on IDEAS

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