Advertisement

Superstatistics with different kinds of distributions in the deformed formalism

  • S. Sargolzaeipor
  • H. Hassanabadi
  • W. S. Chung
Regular Article
  • 35 Downloads

Abstract.

In this article, after first introducing superstatistics, the effective Boltzmann factor in a deformed formalism for modified Dirac delta, uniform, two-level and Gamma distributions is derived. Then we make use of the superstatistics for four important problems in physics and the thermodynamic properties of the system are calculated. All results in the limit case are reduced to ordinary statistical mechanics. Furthermore, effects of all parameters in the problems are calculated and shown graphically.

References

  1. 1.
    M. Jimbo, Lett. Math. Phys. 11, 247 (1986)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    V.G. Drinfeld, in Proceedings of the International Congress of Mathematicians (Berkeley 1986), edited by A.M. Gleason (American Mathematical Society, Providence, 1987)Google Scholar
  3. 3.
    M. Chaichian, D. Ellinas, P. Kulish, Phys. Rev. Lett. 65, 980 (1990)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    M. Chaichian, P. Kulish, J. Lukierski, Phys. Lett. B 237, 401 (1990)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    D. Bonatsos, C. Daskaloyannis, Prog. Part. Nucl. Phys. 43, 537 (1999)ADSCrossRefGoogle Scholar
  6. 6.
    A.J. Macfarlane, J. Phys. A 22, 4581 (1989)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    P.P. Kulish, E.V. Damaskinsky, J. Phys. A 23, L415 (1990)ADSCrossRefGoogle Scholar
  8. 8.
    L. Biedenharn, J. Phys. A 22, L873 (1989)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    S. Sargolzaeipor, H. Hassanabadi, W.S. Chung, Can. J. Phys. 96, 25 (2017)ADSCrossRefGoogle Scholar
  10. 10.
    S. Sargolzaeipor, H. Hassanabadi, A. Boumali, Int. J. Geom. Methods Mod. Phys. 14, 1750112 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    S. Sargolzaeipor, H. Hassanabadi, W.S. Chung, J. Korean Phys. Soc. 70, 557 (2017)ADSCrossRefGoogle Scholar
  12. 12.
    S. Abe, Phys. Rev. E 66, 046134 (2002)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    S. Abe, J. Phys. A 36, 8733 (2003)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    C. Tsallis, A.M.C. Souza, Phys. Rev. E 67, 026106 (2003)ADSCrossRefGoogle Scholar
  15. 15.
    C. Beck, E.G.D. Cohen, Physica A 322, 267 (2003)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    E.G.D. Cohen, Pramana 64, 635 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    P.H. Chavanis, Physica A 359, 177 (2006)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    J.P. Bouchard, M. Potters, Theory of Financial Risk and Derivative Pricing from Statistical Physics to Risk Management (Cambridge University Press, Cambridge, 2003)Google Scholar
  19. 19.
    M. Ausloos, K. Ivanova, Phys. Rev. E 68, 046122 (2003)ADSCrossRefGoogle Scholar
  20. 20.
    H. Touchette, C. Beck, Phys. Rev. E 71, 016131 (2005)ADSCrossRefGoogle Scholar
  21. 21.
    S. Sargolzaeipor, H. Hassanabadi, W.S. Chung, Eur. Phys. J. Plus 133, 5 (2018)CrossRefGoogle Scholar
  22. 22.
    W.S. Chung, H. Sobhani, H. Hassanabadi, Eur. Phys. J. Plus 132, 398 (2017)CrossRefGoogle Scholar
  23. 23.
    C. Tsallis, A.M.C. Souza, Phys. Lett. A 319, 273 (2003)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    G. Wilk, Z.W. lodarczyk, Phys. Rev. Lett. 84, 2770 (2000)ADSCrossRefGoogle Scholar
  25. 25.
    C. Tsallis, J.C. Anjos, E.P. Borges, Phys. Lett. A 310, 372 (2003)ADSCrossRefGoogle Scholar
  26. 26.
    C. Tsallis, Braz. J. Phys. 29, 1 (1999)ADSCrossRefGoogle Scholar
  27. 27.
    C. Beck, Continuum Mech. Thermodyn. 16, 293 (2004)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    C. Tsallis, J. Stat. Phys. 52, 479 (1988)ADSCrossRefGoogle Scholar
  29. 29.
    C. Beck, E.G.D. Cohen, S. Rizzo, Europhys. News 36, 189 (2005)ADSCrossRefGoogle Scholar
  30. 30.
    F. Sattin, L. Salasnich, Phys. Rev. E 65, 035106(R) (2002)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    C. Tsallis, J. Stat. Phys. 52, 479 (1988)ADSCrossRefGoogle Scholar
  32. 32.
    C. Tsallis, R.S. Mendes, A.R. Plastino, Physica A 261, 534 (1998)ADSCrossRefGoogle Scholar
  33. 33.
    S. Abe, Y. Okamoto (Editors), Nonextensive Statistical Mechanics and Its Applications (Springer, Berlin, 2001)Google Scholar
  34. 34.
    R.K. Pathria, Statistical Mechanics, 1st edn. (Pergamon Press, Oxford, 1972)Google Scholar
  35. 35.
    A. Boumali, H. Hassanabadi, Eur. Phys. J. Plus 128, 124 (2013)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • S. Sargolzaeipor
    • 1
  • H. Hassanabadi
    • 1
  • W. S. Chung
    • 2
  1. 1.Faculty of PhysicsShahrood University of ThechnologyShahroodIran
  2. 2.Department of Physics and Research Institute of Natural Science, College of Natural ScienceGyeongsang National UniversityJinjuKorea

Personalised recommendations