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.
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References
D. Lynden-Bell, R.M. Lynden-Bell, Relaxation to a perpetually pulsating equilibrium, J. Stat. Phys. 117, 199 (2004)
F. Calogero, F. Leyvraz, A macroscopic system with undamped periodic compressional oscillations, J. Stat. Phys. 151, 922 (2013)
F. Leyvraz, F. Calogero, A macroscopic system with undamped periodic compressional oscillations, J. Phys.: Conf. Ser. 482, 012027 (2014)
F. Calogero, Classical Many-body Problems Amenable to Exact Treatments, Lecture Notes in Physics Monograph, Vol. M 66 (Springer, 2001)
M. Campisi, P. Hänggi, Fluctuation, dissipation and the arrow of time, Entropy 13, 2024 (2011)
A. Salazar, H. Larralde, F. Leyvraz, Temperature gradients in equilibrium: Small microcanonical systems in an external field, Phys. Rev. E 90, 052127 (2014)
L. Boltzmann, Lectures on Gas Theory (Courier Corporation, 2012)
A. Eddington, The Nature of the Physical World: Gifford Lectures (1927) (Cambridge University Press, 2012)
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)
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)
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)
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)
F. Leyvraz, S. Ruffo, Ensemble inequivalence: A formal approach, Physica A 305, 58 (2002)
F. Leyvraz, S. Ruffo, Ensemble inequivalence in systems with long-range interactions, J. Phys. A 35, 285 (2002)
D. Lynden-Bell, Negative Specific Heat in Astronomy, Physics and Chemistry, Physica A 263, 293 (1999)
J.A. Reyes-Nava, I.L. Garzón, K. Michaelian, Negative heat capacity of sodium clusters, Phys. Rev. B 67, 165401 (2003)
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)
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Leyvraz, F., Larralde, H. Strange systems in statistical mechanics. Eur. Phys. J. Spec. Top. 226, 331–339 (2017). https://doi.org/10.1140/epjst/e2016-60111-2
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DOI: https://doi.org/10.1140/epjst/e2016-60111-2