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ON THE APPLICABILITY OF THE EQUIPARTITION THEOREM

ABSTRACT
Generalization of the equipartition theorem is presented for a broad range of potentials U(x) with quadratic minimum. It is shown, that the equipartition of energy in its standard form appears at the low temperatures limit. For potentials demonstrating the quadratic behavior for large displacements from the equilibrium the equipartition holds also in the high temperature limit. The temperature range of applicability of the equipartition theorem for the potential U = ax2 + bx4 was established.
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PAPER SUBMITTED: 2010-03-11
PAPER REVISED: 2010-03-12
PAPER ACCEPTED: 2010-03-12
DOI REFERENCE: https://doi.org/10.2298/TSCI1003855B
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2010, VOLUME 14, ISSUE 3, PAGES [855 - 858]
REFERENCES
  1. Landau, L., Lifshitz, E., Statistical Physics (Course of Theoretical Physics, vol. 5), Butterworth- -Heinemann, Oxford, UK, 2000
  2. Baierlein, R., Thermal Physics, Cambridge University Press, Cambridge, UK, 2003
  3. van Hemmen, J. L., A Generalized Equipartition Theorem, Physics Letters A, 79 (1980), 1, pp. 25-28
  4. Lawrence, E., Turner, L. E., Jr., Generalized Classical Equipartition Theorem, Am. J. Phys., 44 ( 1976), 1, pp. 104-105
  5. Landsberg, P. T., Generalized Equipartition, Am. J. Phys., 46 (1978), 3, p. 296
  6. Landsberg, P. T., Equipartition for a Relativistic Gas, Am. J. Phys., 60 (1992), 6, p. 561
  7. Lawless, W. N., Energy Equipartition: A Restatement, Am. J. Phys., 32 (1964), 9, pp. 686-687
  8. Martínez, S., et al., On the Equipartition and virial Theorems, Physica A, 305 (2002), 1-2, pp. 48-51
  9. Plastino, A. R., Lima, J. A. S., Equipartition and Virial Theorems within General Thermostatistical Formalisms, Physics Letters A, 260 (1999), 1-2, pp. 46-54
  10. Levashov, V. A., et al., Equipartition Theorem and the Dynamics of Liquids, Physical Review E, 78 (2008), p. 064205
  11. Oberhofer, H., Dellago, Ch., Boresch, St., Single Molecule Pulling with Large Time Steps, Physical Review E, 75 (2007), p. 061106
  12. Fujii, K., Aikawa, Y., Ohoka, K., Structural Phase Transition and Anharmonic Effects in Crystals, Physical Review B, 63 (2001), p. 104107
  13. Gradshteyn, I. S., Ryzhik, I. M., Table of Integrals, Series, and Products, 7th ed., Academic Press, New York, USA, 2007
  14. Arfken, G. B., Weber, H. J., Mathematical Methods for Physicists, 5th ed., Harcourt/Academic Press, San Diego, Cal., USA, 2001

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence