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Geometric Representation of the Group of Entropy Vectors in Nonextensive Statistical Mechanics

  • Elementary Particle Physics and Field Theory
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Russian Physics Journal Aims and scope

A geometric representation of the group of nonextensive entropy vectors in four-dimensional space is derived. The three-dimensional hyperbolic entropy vector and the vector-parameter of hyperbolic angles are determined. A composition law for hyperbolic entropy vectors with quadratic nonlinearity is given and an interrelationship with three distributions characterizing the system is presented.

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References

  1. C. Tsallis, Introduction to Nonextensive Statistical Mechanics. Approaching a Complex World, Springer, New York (2009).

    MATH  Google Scholar 

  2. R. G. Zaripov, Principles of Nonextensive Statistical Mechanics and Geometry of Measures of Disorder and Order [in Russian], Kazan’ State Technical University Press, Kazan’ (2010).

    Google Scholar 

  3. J. Naudts, Generalized Thermostatistics, Springer, London (2011).

    Book  Google Scholar 

  4. N. Bourbaki, Elements of Mathematics: Integration, Springer, Berlin (2004).

    Book  Google Scholar 

  5. R. G. Zaripov, Russ. Phys. J., 48, No. 3, 267 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  6. R. G. Zaripov, Russ. Phys. J., 49, No. 6, 633 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Havrda and F. Charvat, Kybernetika, 3, 30 (1967).

    MATH  MathSciNet  Google Scholar 

  8. Z. Daroczy, Inform. Control, 16, 36 (1970).

    Article  MATH  MathSciNet  Google Scholar 

  9. P. T. Landsberg and V. Vedral, Phys. Lett., A247, 211 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  10. R. G. Zaripov, Russ. Phys. J., 52, No. 2, 200 (2009).

    Article  MathSciNet  Google Scholar 

  11. R. G. Zaripov, Russ. Phys. J., 55, No. 1, 17 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  12. A. Renyi, Probability Theory, North-Holland Publ. Co., Amsterdam (1970).

    Google Scholar 

  13. J. Feder, Fractals, Plenum Press, New York (1988).

    Book  MATH  Google Scholar 

  14. H. Rund, The Differential Geometry of Finsler Spaces, Springer-Verlag, Berlin (1959).

    Book  MATH  Google Scholar 

  15. R. G. Zaripov, in: Recent Problems in Field Theory 2005–2006 [in Russian], edited by A. V. Aminova, Kazan’ State University Publishing House, Kazan’ (2007).

    Google Scholar 

  16. D. G. Pavlov, Gh. Atanasiu, and V. Balan, eds., Space-Time Structure. Algebra and Geometry, Lilia-Print, Moscow (2007).

    Google Scholar 

  17. V. Balan, G. Yu. Bogoslovsky, S. S. Kokarev, et al., J. Modern Phys., 3, No. 9A, 1314 (2012).

    Article  Google Scholar 

  18. F. Catoni, R. Cannata, and P. Zampetti, Adv. Appl. Clifford Algebr., 16, 1 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  19. R. G. Zaripov, Russ. Phys. J., 57, No. 1, 6 (2014).

    Article  MATH  Google Scholar 

  20. B. Riemann, Abhandlungen der Königl. Gesellschaft der Wissenschaften zu Göttingen, 13, 14 (1867).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mechanics and Machine Building of the Kazan’ Scientific Center of the Russian Academy of Sciences, Kazan’, Russia

    R. G. Zaripov

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  1. R. G. Zaripov
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Correspondence to R. G. Zaripov.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 3–9, July, 2014.

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Zaripov, R.G. Geometric Representation of the Group of Entropy Vectors in Nonextensive Statistical Mechanics. Russ Phys J 57, 861–869 (2014). https://doi.org/10.1007/s11182-014-0318-3

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  • DOI: https://doi.org/10.1007/s11182-014-0318-3

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