Journal of Statistical Physics

, Volume 72, Issue 3–4, pp 519–537 | Cite as

Molecular dynamics and time reversibility

  • D. Levesque
  • L. Verlet


We present a time-symmetrical integer arithmetic algorithm for numerical (molecular dynamics) simulations of classical fluids. This algorithm is used to illustrate, through concrete examples, that time-asymmetric evolutions are typical for systems of many particles evolving according to reversible microscopic dynamics and to calculate the asymptotic behavior of the velocity autocorrelation function with an improved accuracy. The equivalence between equilibrium time averages and microcanonical ensemble averages is checked via two new sampling methods for computing microcanonical averages of classical systems.

Key words

Numerical simulations irreversibility Monte Carlo methods microcanonical ensemble long-time tail 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. L. Lebowitz, Lecture presented at the Conference on Physical Origin of Time Asymmetry, Mazagon, Spain (1991).Google Scholar
  2. 2.
    K. Popper,Unended Quest (Collins, Glasgow, 1978).Google Scholar
  3. 3.
    I. Prigogine and I. Stengers,Entre le temps et l'éternité (Fayard, Paris, 1988).Google Scholar
  4. 4.
    J. Orban and A. Bellemans,Phys. Lett. 224:620 (1967).Google Scholar
  5. 5.
    L. Verlet,Phys. Rev. 159:98 (1967).Google Scholar
  6. 6.
    D. Levesque and W. T. Ashurst,Phys. Rev. Lett. 33:277 (1974).Google Scholar
  7. 7.
    J. J. Erpenbeck and W. W. Wood,Phys. Rev. A 26:1648 (1982);32:412 (1985); J. J. Erpenbeck,Phys. Rev. A 35:218 (1987).Google Scholar
  8. 8.
    J. R. Ray,Phys. Rev. A 44:4061 (1991).Google Scholar
  9. 9.
    H. Creutz,Phys. Rev. Lett. 50:1411 (1983).Google Scholar
  10. 10.
    N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller,J. Chem. Phys. 21:1087 (1953).Google Scholar
  11. 11.
    A. Rahman,Phys. Rev. 136:405 (1964).Google Scholar
  12. 12.
    J. Delambre,Mem. Acad. Turin 5:143 (1790–1793).Google Scholar
  13. 13.
    W. E. Milne,Numerical Solution of Differential Equations (Wiley, New York, 1960).Google Scholar
  14. 14.
    C. Störmer,Arch. Sci. Phys. Nat. Genève (1907).Google Scholar
  15. 15.
    C. Störmer, inCongress International Mathematiques Strasbourg (Toulouse, 1921), p. 24.Google Scholar
  16. 16.
    W. G. Hoover,Molecular Dynamics (Springer, 1986), p. 3.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • D. Levesque
    • 1
  • L. Verlet
    • 1
  1. 1.Laboratoire de Physique Théorique et Hautes Energies (Laboratoire associé au Centre National de la Recherche Scientifique)Université de Paris XIOrsay CedexFrance

Personalised recommendations