Skip to main content
SpringerLink
Log in

The origin of computational statistical mechanics in France

  • Published:
The European Physical Journal H Aims and scope Submit manuscript

Abstract

The two main methodologies of computational Statistical Mechanics, namely the stochastic Monte Carlo and the deterministic Molecular Dynamic methods, were developed in the USA in the mid 1950’s. In the present paper we show how these “computer experiments” migrated to Europe in the 60s, and first bloomed at the Orsay Science Faculty, before spreading throughout Europe. Collaborations between the Orsay group, led by Loup Verlet, and pioneering groups in the USA and Europe are pointed out. Finally it is shown how the celebrated Verlet algorithm for the integration of classical equations of motion can be traced back to Isaac Newton.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alder B.J. and Wainwright T.E. 1957. Phase Transition for a Hard Sphere System. J. Chem. Phys. 27: 1208–1209

    Article  ADS  Google Scholar 

  2. Alder B.J. and Wainwright T.E. 1959. Studies in Molecular Dynamics. I. General Method. J. Chem. Phys. 31: 459–466

    ADS  MathSciNet  Google Scholar 

  3. Alder B.J. and Wainwright T.E. 1967. Velocity Autocorrelation for Hard Spheres. Phys. Rev. Lett. 18: 988–990

    Article  ADS  Google Scholar 

  4. Alder B.J., Weis J.J. and Strauss H.L. 1973. Depolarization of Light in Atomic Fluids. Phys. Rev. A 7: 281–284

    Article  ADS  Google Scholar 

  5. Barojas J., Levesque D. and Quentrec B. 1973. Simulation of Diatomic Homonuclear Liquids. Phys. Rev. A 7: 1092–1105

    Article  ADS  Google Scholar 

  6. Baxter R.J. 1968. Ornstein-Zernike Relation for a Disordered Fluid. Aust. J. Phys. 21: 563–569

    Article  ADS  Google Scholar 

  7. Binder K. and Rauch H. 1968. Calculation of spin-correlation functions in a ferromagnet with a Monte Carlo method. Phys. Lett. A 27: 247–248

    Article  ADS  Google Scholar 

  8. Cooley J.W. and Tukey J.W. 1965. An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation 19: 297–301.s

    Article  MathSciNet  MATH  Google Scholar 

  9. Drell S.D. and Verlet L. 1955. Multiple Scattering Corrections in π± Deuteron Scattering. Phys. Rev. 99: 849–857

    Article  ADS  Google Scholar 

  10. Frenkel D. and Mulder B. 1985. The Hard Ellipsoid of Revolution Fluid: I. Monte-Carlo Simulations. Mol. Phys. 55: 1171–1192

    Article  ADS  Google Scholar 

  11. Hansen J.P. and Levesque D. 1968. Ground State of Solid Helium-4 and -3. Phys. Rev. 165: 293–300

    Article  ADS  Google Scholar 

  12. Hansen J.P., Jancovici B. and Schiff D. 1972. Phase Diagram of a Charged Bose Gas. Phys. Rev. Lett. 29: 991–995

    Article  ADS  Google Scholar 

  13. Hansen J.P. 1973. Statistical Mechanics of Dense Ionized Matter. I. Equilibrium Properties of Classical One-component Plasma. Phys. Rev. A 8: 3096–3109

    Article  ADS  Google Scholar 

  14. Hansen J.P., McDonald I.R. and Pollock E.L. 1975. Statistical Mechanics of Dense Ionized Matter. III. Dynamical Properties of Classical One-component Plasma. Phys. Rev. A 21: 1025–1039

    Article  ADS  Google Scholar 

  15. Jastrow R. 1955. Many-Body Problem with Strong Forces. Phys. Rev. 98: 1479–1484

    Article  ADS  MATH  Google Scholar 

  16. Kalos M.H., Levesque D. and Verlet, L. 1974. Helium at Zero Temperature with Hard Sphere and Other Forces. Phys. Rev. A 9: 2178–2195

    Article  ADS  Google Scholar 

  17. Lebowitz J., Percus J.K. and Verlet L. 1967. Ensemble Dependence of Fluctuations with Application to Machine Computations. Phys. Rev. 153: 250–254

    Article  ADS  Google Scholar 

  18. Levesque D., Tu Khiet, Schiff D. and Verlet L. 1965. On the Ground State of Liquid and Solid He4 at Zero Temperature. Preprint (unpublished)

  19. Levesque D. and Ashurst W. 1974. Long Time Behavior of the Velocity Autocorrelation Function for a Fluid of Soft Repulsive Particles. Phys. Rev. Lett. 33: 277–280

    Article  ADS  Google Scholar 

  20. Mareschal M. 2018. Early Years of Computational Statistical Mechanics. Eur. Phys. J. H. 43: 293–302

    Article  Google Scholar 

  21. McDonald I.R. and Singer K. 1967. Calculation of thermodynamic properties of liquid argon from Lennard-Jones parameters by a Monte Carlo method. Disc. Faraday Soc 43: 40–49

    Article  Google Scholar 

  22. McMillan W.E. 1965. Ground State of Liquid He4. Phys. Rev. A 138: 442–452

    Article  ADS  Google Scholar 

  23. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H. and Teller E. 1953. Equation of State Calculations by Fast Computing Machines. J. Chem. Phys. 23: 1087–1093

    Article  ADS  Google Scholar 

  24. Newton I. 1883, Philosophiae naturalis principia mathematica. Glasguae, Impensis T.T et J. Tegg, Londini. (http://books.google.com)

  25. Onsager L. 1944. Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition. Phys. Rev. 65: 117–149

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Ornstein L.S. and Zernike F. 1914. Accidental deviations of density and opalescence at the critical point of a single substance. Royal Netherlands Academy of Arts and Sciences Proceedings 17: 793–806

    Google Scholar 

  27. Percus J.K. and Yevick G.J. 1958. Analysis of Classical Statistical Mechanics by Means of Collective Coordinates. Phys. Rev. 110: 1–13

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. Principia Translation. 1934, Newton’s Principia Motte’s translation 1729 revised by Florian Cajori, University of California Press, Berkeley, Los Angeles, London, p. 40–41: For suppose the time to be divided into equal parts, and in the first part of that time let the body by its innate force describe the right line AB. In the second part of that time, the same would (by Law "i"), if not hindered, proceed directly to c, along the line Bc equal to AB; so that by the radii AS, BS, cS, drawn to the centre, the equal areas ASB, BSc, would be described. But when the body is arrived at B, suppose that a centripetal force acts at once with a great impulse, and, turning aside the body from the right line Bc, compels it afterwards to continue its motion along the right line BC. Draw cC parallel to BS meeting BC in C; andat the end of the second part of the time, the body (by Cor. "i" of the Laws) will befound in C, ...

  29. Rahman A. 1964. Correlations in the Motion of Atoms in Liquid Argon. Phys. Rev. A 136: 405–409

    Article  ADS  Google Scholar 

  30. Rosenbluth M.N. and Rosenbluth A.W. 1955. Monte Carlo Calculation of the Average Extension of Molecular Chains. J. Chem. Phys. 23: 356–360

    Article  ADS  Google Scholar 

  31. Stauffer D. 1985. Introduction to Percolation Theory. Taylor and Francis, London

  32. Schiff D. and Verlet L. 1967. Ground State of Liquid Helium-4 and Helium-3. Phys. Rev. 160: 208–219

    Article  ADS  Google Scholar 

  33. Schiff D. 1969. Computer “Experiments” on Liquid Metals. Phys. Rev. 186: 151–160

    Article  ADS  Google Scholar 

  34. Thiele E. J. 1963. Equation of State for Hard Spheres. J. Chem. Phys. 39: 474–479

    Article  ADS  Google Scholar 

  35. Verlet L. 1960. On the theory of classical fluids. Il Nuovo Cimento 18: 77–101

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Verlet L. and Levesque D. 1962. On the theory of classical fluids II. Physica 28: 1124–1142

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Verlet L. 1964. On the theory of classical fluids-III. Physica 30: 95–104

    Article  ADS  MathSciNet  Google Scholar 

  38. Verlet L. 1965. On the theory of classical fluids-IV. Physica 31: 959–966

    Article  ADS  MathSciNet  Google Scholar 

  39. Verlet L. 1967. Computer “Experiments” on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules. Phys. Rev. 159: 98–104

    Google Scholar 

  40. Verlet L. and Schiff D. 1974. Tribune libre : Faut-il continuer la recherche scientifique ? La Recherche nov. 1974: 924

    Google Scholar 

  41. Verlet L. 1993. La Malle de Newton, Bibliothèque des Sciences Humaines, Gallimard, Paris.

  42. Verlet L. 2007. Chimères et Paradoxes, Les Éditions du Cerf, Paris.

  43. Vieillard-Baron J. 1972. Phase Transitions of the Classical Hard-Ellipse System. J. Chem. Phys. 56: 4729–4744

    Article  ADS  Google Scholar 

  44. Wertheim M.S. 1963. Exact Solution of the Percus-Yevick Integral Equation for Hard Spheres. Phys. Rev. Lett. 10: 321–323

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. Wood W.W. and Parker F.R. 1957a. Monte Carlo Equation of State of Molecules Interacting with the Lennard-Jones Potential. I. A Supercritical Isotherm at about Twice the Critical Temperature. J. Chem. Phys. 27: 720–734

    Google Scholar 

  46. Wood W.W. and Jacobson J.D. 1957b. Preliminary Results from a Recalculation of the Monte Carlo Equation of State of Hard Spheres. J. Chem. Phys. 27: 1207–1208

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique Théorique, Bâtiment 210, Université Paris-Saclay, 91400, Orsay, France

    D. Levesque

  2. Laboratoire Phénix, Université Pierre et Marie Curie, 75005, Paris, France

    J. P. Hansen

  3. Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK

    J. P. Hansen

Authors
  1. D. Levesque
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. P. Hansen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Levesque.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Levesque, D., Hansen, J.P. The origin of computational statistical mechanics in France. EPJ H 44, 37–46 (2019). https://doi.org/10.1140/epjh/e2018-90041-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjh/e2018-90041-y

Search

Navigation