Journal of Statistical Physics

, Volume 107, Issue 5–6, pp 1143–1166 | Cite as

Statistical Mechanics of Classical Systems with Distinguishable Particles

  • Robert H. Swendsen


The properties of classical models of distinguishable particles are shown to be identical to those of a corresponding system of indistinguishable particles without the need for ad hoc corrections. An alternative to the usual definition of the entropy is proposed. The new definition in terms of the logarithm of the probability distribution of the thermodynamic variables is shown to be consistent with all desired properties of the entropy and the physical properties of thermodynamic systems. The factor of 1/N! in the entropy connected with Gibbs' Paradox is shown to arise naturally for both distinguishable and indistinguishable particles. These results have direct application to computer simulations of classical systems, which always use distinguishable particles. Such simulations should be compared directly to experiment (in the classical regime) without “correcting” them to account for indistinguishability.

entropy Gibbs' paradox distinguishability 


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  1. 1.
    For two recent examples, see R. K. Pathria, Statistical Mechanics, 2nd ed. (Butterworth-Heinemann, Oxford, 2001), p. 25, and L. Kadanoff, Statistical Physics, Statics, Dynamics and Renormalization (World Scientific, Singapore, 2000), p. 14.Google Scholar
  2. 2.
    L. Boltzmann, Sitzb. Akad. Wiss. Wien 76:373 (1877); Wissenschaftliche Abhandlungen von Ludwig Boltzmann, Vol. II (Chelsea, New York, 1968), pp. 164–223.Google Scholar
  3. 3.
    J. W. Gibbs, Elementary Principles in Statistical Mechanics (Yale University Press, New Haven, 1902); reprinted by (Dover, New York, 1960).Google Scholar
  4. 4.
    N. G. van Kampen, The Gibbs paradox, in Essays in Theoretical Physics, W. E. Parry, ed. (Pergamon, Oxford, 1984), pp. 303–312.Google Scholar
  5. 5.
    E. T. Jaynes, The Gibbs Paradox' in Maximum-Entropy and Bayesian Methods, G. Erickson, P. Neudorfer, and C. R. Smith, eds. (Kluwer, Dordrecht), p. 992.Google Scholar
  6. 6.
    H. B. Callen, Thermodynamics and an Introduction to Thermostatistics (Wiley, New York, 1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Robert H. Swendsen
    • 1
  1. 1.Physics DepartmentCarnegie Mellon UniversityPittsburghPennsylvania

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