The European Physical Journal Special Topics

, Volume 226, Issue 3, pp 331–339 | Cite as

Strange systems in statistical mechanics

Regular Article
  • 46 Downloads
Part of the following topical collections:
  1. Nonlinearity, Nonequilibrium and Complexity: Questions and Perspectives in Statistical Physics

Abstract

A number of rather unexpected behaviours in various systems are reviewed. Namely, it is shown that a macroscopic system having chaotic dynamics may nevertheless display undamped harmonic radial oscillations. Next, we show that small systems in an external field may have spatially dependent kinetic temperatures in equilibrium. Further, we can also show that the kinetic temperatures of different particle species in the same region of space will in general not assume the same values. Finally, we discuss the remarkable way in which the zero’th law of thermodynamics can sometimes appear to be violated in systems having long-range interactions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Lynden-Bell, R.M. Lynden-Bell, Relaxation to a perpetually pulsating equilibrium, J. Stat. Phys. 117, 199 (2004)ADSMathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    F. Calogero, F. Leyvraz, A macroscopic system with undamped periodic compressional oscillations, J. Stat. Phys. 151, 922 (2013)ADSMathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    F. Leyvraz, F. Calogero, A macroscopic system with undamped periodic compressional oscillations, J. Phys.: Conf. Ser. 482, 012027 (2014)MATHGoogle Scholar
  4. 4.
    F. Calogero, Classical Many-body Problems Amenable to Exact Treatments, Lecture Notes in Physics Monograph, Vol. M 66 (Springer, 2001)Google Scholar
  5. 5.
    M. Campisi, P. Hänggi, Fluctuation, dissipation and the arrow of time, Entropy 13, 2024 (2011)ADSMathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    A. Salazar, H. Larralde, F. Leyvraz, Temperature gradients in equilibrium: Small microcanonical systems in an external field, Phys. Rev. E 90, 052127 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    L. Boltzmann, Lectures on Gas Theory (Courier Corporation, 2012)Google Scholar
  8. 8.
    A. Eddington, The Nature of the Physical World: Gifford Lectures (1927) (Cambridge University Press, 2012)Google Scholar
  9. 9.
    J. Loschmidt, Über den Zustand des Wärmegleichgewichtes eines Systems von Körpern mit Rücksicht auf die Schwerkraft, Sitzungsberichte der mathematisch-naturwissenschaftlichen Classe LXXIII 11, 128 (1876)Google Scholar
  10. 10.
    A. Ramí rez-Hernández, H. Larralde, F. Leyvraz, Violation of the Zeroth Law of Thermodynamics in Systems with Negative Specific Heat, Phys. Rev. Lett. 100, 120601 (2008)ADSCrossRefGoogle Scholar
  11. 11.
    A. Ramí rez-Hernández, H. Larralde, F. Leyvraz, Systems with negative specific heat in thermal contact: Violation of the zeroth law, Phys. Rev. E 78, 061133 (2008)ADSCrossRefGoogle Scholar
  12. 12.
    E.M. Pearson, T. Halicioglu, W.A. Tiller, Laplace-transform technique for deriving thermodynamic equations from the classical microcanonical ensemble, Phys. Rev. A 32, 3030 (1985)ADSCrossRefGoogle Scholar
  13. 13.
    F. Leyvraz, S. Ruffo, Ensemble inequivalence: A formal approach, Physica A 305, 58 (2002)ADSMathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    F. Leyvraz, S. Ruffo, Ensemble inequivalence in systems with long-range interactions, J. Phys. A 35, 285 (2002)ADSMathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    D. Lynden-Bell, Negative Specific Heat in Astronomy, Physics and Chemistry, Physica A 263, 293 (1999)ADSCrossRefGoogle Scholar
  16. 16.
    J.A. Reyes-Nava, I.L. Garzón, K. Michaelian, Negative heat capacity of sodium clusters, Phys. Rev. B 67, 165401 (2003)ADSCrossRefGoogle Scholar
  17. 17.
    A. Campa, A. Giansanti, D. Mukamel, S. Ruffo, Dynamics and thermodynamics of rotators interacting with both long-and short-range couplings, Physica A 365, 120 (2006)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2017

Authors and Affiliations

  1. 1.Instituto de Ciencias Físicas—Universidad Nacional Autónoma de MéxicoMorelosMexico
  2. 2.Centro Internacional de CienciasMorelosMexico

Personalised recommendations