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Group of energies and its representations in nonextensive statistical mechanics

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Russian Physics Journal Aims and scope

The Abel groups of macroscopic and free energies are determined in the context of equilibrium nonextensive thermodynamics. Matrix and algebraic group representations and properties of composition laws are given.

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References

  1. C. Tsallis, Introduction to Nonextensive Statistical Mechanics. Approaching a Complex World, Springer, New York (2009); http://www.cbpf.br/GrupPesq/StatisticalPhys/TEMUCO.pdf.

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

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

    Book  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  7. J. Feder, Fractals [Russian translation], Mir, Moscow (1991).

    Google Scholar 

  8. R. G. Zaripov, Zh. Tekh. Fiz., 76, No. 11, 1–5 (2006).

    Google Scholar 

  9. R. G. Zaripov, Russ. Phys. J., 48, No. 3, 267–274 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  10. R. G. Zaripov, Russ. Phys. J., 49, No. 6, 633–641 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  11. I. J. Taneja, in: Advances in Imaging and Electron Physics, Vol. 91, P. W. Hawkes, ed., Academic Press, London (1995), pp. 37–135; http://www.mtm.ufsc.br/~taneja/book/

  12. R. G. Zaripov, New Measures and Methods in Information Theory [in Russian], Publishing House of Kazan’ State Technical University, Kazan’ (2005).

  13. R. G. Zaripov, Russian Phys. J., 52, No. 2, 200–209 (2009).

    Article  MathSciNet  ADS  Google Scholar 

  14. R. G. Zaripov, Russian Phys. J., 55, No. 1, 17–24 (2012).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Q. A. Wang and A. Le Méhauté, J. Math. Phys., 43, 5079 (2002).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. M. A. Lavrent’ev and B. V. Shabat, Problems of Hydrodynamics and Their Mathematical Models [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  17. F. Catoni, R. Cannata, V. Catoni, and P. Zampetti, Adv. Appl. Cliff. Algebr., 14, No. 1, 47 (2004).

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to R. G. Zaripov.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 62–67, October, 2012.

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Zaripov, R.G. Group of energies and its representations in nonextensive statistical mechanics. Russ Phys J 55, 1169–1176 (2013). https://doi.org/10.1007/s11182-013-9939-1

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  • DOI: https://doi.org/10.1007/s11182-013-9939-1

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