THERMAL SCIENCE

International Scientific Journal

Edward Bormashenko

,

Oleg Gendelman

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.
KEYWORDS
equipartition of energy, saddle point method, quadratic potential
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 No. 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
PDF VERSION [DOWNLOAD]
On the applicability of the equipartition theorem

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, 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