Russian Physics Journal

, Volume 62, Issue 1, pp 40–48 | Cite as

Entropy Group in Parastatistics of Quantum Nonextensive Systems

  • R. G. ZaripovEmail author

An Abelian group of entropies is defined and its representations for quantum nonextensive systems with a composition law having quadratic nonlinearity are determined. Its most general properties are given, and a connection with the hyperbolic angle is established. An extension of parastatistics is presented, in particular cases of which known results follow.


nonextensivity entropy group algebra parastatistics 


  1. 1.
    R. G. Zaripov, New Measures and Methods in Information Theory [in Russian], Kazan State Technical University Press, Kazan (2005).Google Scholar
  2. 2.
    C. Tsallis, Introduction to Nonextensive Statistical Mechanics. Approaching a Complex World, Springer, New York (2009).zbMATHGoogle Scholar
  3. 3.
    R. G. Zaripov, Principles of Non-Extensive Statistical Mechanics and Geometry of Measures of Disorder and Order [in Russian], Kazan State Technical Univ. Press, Kazan (2010).Google Scholar
  4. 4.
    J. Naudts, Generalized Thermostatistics, Springer, Berlin (2011).CrossRefzbMATHGoogle Scholar
  5. 5.
    R. G. Zaripov, Russ. Phys. J., 59, No. 12, 2059 (2017).CrossRefGoogle Scholar
  6. 6.
    R. G. Zaripov, Russ. Phys. J., 60, No. 5, 789 (2017).CrossRefGoogle Scholar
  7. 7.
    R. G. Zaripov, Russ. Phys. J., 61, No. 1, 123 (2018).CrossRefGoogle Scholar
  8. 8.
    S. N. Bose, Zeitschrift für Physik, 26, 178 (1924).CrossRefGoogle Scholar
  9. 9.
    G. Gentile, Nuovo Cimento, 19, No. 4, 109 (1942).CrossRefGoogle Scholar
  10. 10.
    R. G. Zaripov, Adv. Appl. Clifford Algebras, 27, 1741 (2017).MathSciNetCrossRefGoogle Scholar
  11. 11.
    A. Rényi, Probability Theory, North-Holland Publ. Co., Amsterdam (1970).zbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Mechanics and Machine Building of the Kazan Scientific Center of the Russian Academy of SciencesKazanRussia

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