Abstract
It is usually assumed, in classical statistical mechanics, that the temperature should coincide, apart from a suitable constant factor, with the mean kinetic energy of the particles. We show that this is not the case for Fermi–Pasta–Ulam systems, in conditions in which energy equipartition between the modes is not attained. We find that the temperature should be rather identified with the mean value of the energy of the low frequency modes.
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REFERENCES
P. Bocchieri, A. Scotti, B. Bearzi, and A. Loinger, Phys. Rev. A 2:2012(1970); L. Galgani and A. Scotti, Phys. Rev. Lett. 28:1173(1972); R. Livi, M. Pettini, S. Ruffo, and A. Vulpiani, Phys. Rev. A 31:2740(1985).
L. Berchialla, L. Galgani, and A. Giorgilli, Localization of energy in FPU chains, Discrete Contin. Dynam. Systems, in print (2003).
R. Livi, M. Pettini, S. Ruffo, and A. Vulpiani, J. Stat. Phys. 48:539(1987).
A. Perronace and A. Tenenbaum, Phys. Rev. E 51:100(1998); A. Perronace and A. TenenbaumPhys. Rev. E 51:6215(1998).
A. Carati and L. Galgani, J. Stat. Phys. 94:859(1999).
P. T. Landsberg, Thermodynamics (Interscience, New York, 1961).
L. Landau and E. Teller, Physik. Z. Sowjetunion 10:34(1936); also in L. Landau and E. TellerCollected Papers of L. D. Landau, D. Ter Haar, ed. (Pergamon Press, Oxford, 1965); G. Benettin, A. Carati, and G. Gallavotti, Nonlinearity 10:65-79 (1995).
A. Carati, L. Galgani, and B. Pozzi, Phys. Rev. Lett. 90:010601(2003).
J.-P. Eckmann, C.-A. Pillet, and L. Rey-Bellet, Comm. Math. Phys. 201:657–697 (1999).
F. Bonetto, J. L. Lebowitz, and L. Rey-Bellet, in Mathematical Physics 2000, A. Fokas, A. Grigoryan, T. Kibble, and B. Zegarlinski, eds. (World Scientific, Singapore, 2000).
H. Poincarè, J. Phys. Th. App. 5:369(1906).
V. V. Kozlov, Contribution to the Conference for the Centennial of Kolmogorov's Birth (Moscow, June 2003). See also: V. V. Kozlov, Thermal Equilibrium by Gibbs and Poincarè (in russian) (Institute of Computer Investigations, Moscow-Pjevsk, 2002).
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Carati, A., Cipriani, P. & Galgani, L. On the Definition of Temperature in FPU Systems. Journal of Statistical Physics 115, 1101–1112 (2004). https://doi.org/10.1023/B:JOSS.0000022378.52789.b6
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DOI: https://doi.org/10.1023/B:JOSS.0000022378.52789.b6