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2006 | 4 | 3 | 363-368

Article title

Lévy-statistics for partially equilibrated systems


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We examine deviations from Boltzmann-Gibbs statistics for a certain class of partially equilibrated systems of finite size. We find that such systems are characterized by the Lévy distribution whose non-extensivity parameter is related to the number of internally equilibrated subsystems and to correlations among them. This concept is applicable to relativistic heavy ion collisions.










Physical description


1 - 9 - 2006
1 - 9 - 2006


  • Department of Physics and Astronomy, Drake University, Des Moines, IA, 50311, USA


  • [1] C. Tsallis: “Possible generalization of Boltzmann-Gibbs entropy”, J. Stat. Phys., Vol. 52, (1988), p. 479; C. Tsallis, S.V.F. Levy, A.M.C. Souza, and R. Maynard: “Statistical-mechanical foundation of the Ubiquity of Lévy distributions in nature”, Phys. Rev. Lett., Vol. 75, (1995), p. 3589. http://dx.doi.org/10.1007/BF01016429[Crossref]
  • [2] G. Wilk and Z. Włodarczyk: “Interpretation of the nonextensivity parameter q in some applications of Tsallis statistics and Lévy distributions”, Phys. Rev. Lett., Vol. 84, (2000), p. 2770; this work addresses only the q > 1 case. The generalization to q < 1 is provided in G. Wilk and Z. Włodarczyk: “The imprints of nonextensive statistical mechanics in high-energy collisions, in classical and quantum complexity and nonextensive thermodynamics” Chaos, Solitons, and Fractals Vol. 13, (2002), p. 547. http://dx.doi.org/10.1103/PhysRevLett.84.2770
  • [3] C. Tsallis: “Nonextensive physics: a possible connection between generalized statistical mechanics and quantum groups”, Phys. Lett. A, Vol. 195, (1994), p. 539; S. Abe: “A note on the q-deformation theoretic aspect of the generalized entropies in nonextensive physics”, Phys. Lett. A, Vol. 224, (1997), p. 326; R.S. Johal: “q-Calculus and entropy in nonextensive statistical physics”, Phys. Rev. E, Vol, 58, (1998), p. 4147; M.R. Ubriaco: “Thermodynamics of boson and fermion systems with fractal distribution functions”, Phys. Rev. E, Vol. 60, (1999), p. 165. http://dx.doi.org/10.1016/0375-9601(94)90037-X[Crossref]
  • [4] G. Kaniadakis, A. Lavagno, M. Lissia and P. Quarati: “Nonextensive statistical effects in nuclear physics problems”, Proceedings of 7th Convegno su Problemi di Fisica Nucleare Theorica, Cortona, Italy, 19–21 Oct 1998, In: A. Fabrocini, G. Pisent and S. Rosati (Eds.): Perspectives on theoretical nuclear physics, p. 293; G. Kaniadakis, A. Lavagno and P. Quarati: “Generalized statistics and solar neutrinos”, Phys. Lett. B, Vol. 369, (1996), p. 308.
  • [5] O.V. Utyuzh, G. Wilk and Z. Włodarczyk: “The fractal properties of the source and BEC”, Czech J. Phys., Vol. 50/S2, (2000), p. 132.
  • [6] G. Wilk and Z. Włodarczyk: “Do we observe Lévy flights in cosmic rays?”, Nucl. Phys., Vol. B, Proc. Suppl., Vol. 75A, (1999), p. 191.
  • [7] T.H. Solomon, E.R. Weeks and H.L. Swinney: “Observation of anomalous diffusion and Lévy flights in a two-dimensional rotating flow”, Phys. Rev. Lett., Vol. 71, (1993), p. 3975. http://dx.doi.org/10.1103/PhysRevLett.71.3975[Crossref]
  • [8] F. Bardou, J.P. Bouchaud, O. Emile, A. Aspect and C. Cohen-Tannoudji: “Subrecoil laser cooling and Lévy flights”, Phys. Rev. Lett., Vol. 72, (1994), p. 203. http://dx.doi.org/10.1103/PhysRevLett.72.203[Crossref]
  • [9] G. Kaniadakis, A. Lavagno and P. Quarati: “Generalized fractional statistics”, Mod. Phys. Lett., Vol. B10, (1996), p. 497; U. Tirnakli and D.F. Torres: “Exact and approximate results of non-extensive quantum statistics”, Eur. Phys. J., Vol. B14, (2000), p. 691. [Crossref]
  • [10] D.H.E. Gross and E. Votyakov: “Phase transitions in ’small’ systems”, Eur. Phys. J., Vol. B15, (2000), p. 115. [Crossref]
  • [11] H.B. Prosper: “Temperature fluctuations in a heat bath”, Am. J. Phys., Vol. 61(1), (1992), p. 54. http://dx.doi.org/10.1119/1.17410[Crossref]
  • [12] Special issue, Braz. J. Phys., Vol. 29(1), (1999); also available at the URL: http://www.sbfisica.org.br/bjp/vol29n1.htm
  • [13] This ensemble differs from the polythermal ensemble proposed by G.D. Phillies: “The polythermal ensemble: A rigorous interpretation of temperature fluctuations in statistical mechanics”, Am. J. Phys., Vol. 52(7), (1984), p. 629 and which is related to global temperature fluctuations. Interestingly, in this article, Phillies has shown that β = 1/λ is a more fundamental physical variable for a small system than λ = T. http://dx.doi.org/10.1119/1.13583[Crossref]
  • [14] L.D. Landau and E.M. Lifshitz: Course of Theoretical Physics: Statistical Physics, Pergamon Press, 1980.
  • [15] C. Beck and E.G.D. Cohen: “Superstatistics”, Physica, Vol. A322, (2003), p. 267.
  • [16] C. Tsalis and A.M.C. Souza: “Constructing a statistical mechanics for Beck-Cohen superstatistics”, Phys. Rev. E, Vol. 67, (2003), art. 026106.
  • [17] T.S. Biro and A. Jakovac: “Power-law tails from multiplicative noise”, Phys. Rev. Lett., Vol. 94, (2005), art. 132302.
  • [18] D.B. Walton and J. Rafelski: “Equilibrium distribution of heavy quarks in Fokker-Planck dynamics”, Phys. Rev. Lett., Vol. 84, (2000), p. 31. http://dx.doi.org/10.1103/PhysRevLett.84.31[Crossref]
  • [19] M. Biyajima, M. Kaneyama, T. Mizoguchi and G. Wilk: “Analyses of κ at RHIC by means of some selected statistical and stochastic models”, Eur. Phys. J., Vol. C40, (2005), p. 243; T.S. Biro, G. Purcsel, G. Gyorgyi and A. Jakovac: “A non-conventional description of quark matter”, J. Phys., Vol. G 31, (2005), p. S759. http://dx.doi.org/10.1140/epjc/s2005-02140-2[Crossref]

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