Skip to main content
SpringerLink
Log in

Equilibrium and nonequilibrium properties of systems with long-range interactions

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

Abstract

We briefly review some equilibrium and nonequilibrium properties of systems with long-range interactions. Such systems, which are characterized by a potential that weakly decays at large distances, have striking properties at equilibrium, like negative specific heat in the microcanonical ensemble, temperature jumps at first order phase transitions, broken ergodicity. Here, we mainly restrict our analysis to mean-field models, where particles globally interact with the same strength. We show that relaxation to equilibrium proceeds through quasi-stationary states whose duration increases with system size. We propose a theoretical explanation, based on Lynden-Bell’s entropy, of this intriguing relaxation process. This allows to address problems related to nonequilibrium using an extension of standard equilibrium statistical mechanics. We discuss in some detail the example of the dynamics of the free electron laser, where the existence and features of quasi-stationary states is likely to be tested experimentally in the future. We conclude with some perspectives to study open problems and to find applications of these ideas to dipolar media.

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. Edited by T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens, Dynamics and thermodynamics of systems with long-range interactions (Springer, Berlin, 2001)

    Google Scholar 

  2. L. Onsager, Il Nuovo Cimento (Suppl.) 6, 279 (1949)

    Article  MathSciNet  Google Scholar 

  3. V.A. Antonov, Leningrad Univ. 7, 135 (1962) [translation in IAU Symposium 113, 525 (1995)]; D. Lynden-Bell, R. Wood, Mon. Not. R. Astr. Soc. 138, 495 (1968); P. Hertel, W. Thirring, Ann. Phys. 63, 520 (1971)

    ADS  Google Scholar 

  4. A. Campa, S. Ruffo, H. Touchette, Physica A 385, 233 (2007)

    Article  ADS  Google Scholar 

  5. J. Barré, D. Mukamel, S. Ruffo, Phys. Rev. Lett. 87, 030601 (2001)

    Article  ADS  Google Scholar 

  6. D. Mukamel, S. Ruffo, N. Schreiber, Phys. Rev. Lett. 95, 240604 (2005)

    Article  ADS  Google Scholar 

  7. M.K.H. Kiessling, J.L. Lebowitz, Lett. Math. Phys. 42, 43 (1997), and references therein; R.S. Ellis, K. Haven, B. Turkington, J. Stat. Phys. 101, 999 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. I. Ispolatov, E.G.D. Cohen, Phys. A 295, 475 (2001)

    Article  MATH  Google Scholar 

  9. J. de Luca, A.J. Lichtenberg, S. Ruffo, Phys. Rev. E 60, 3781 (1999)

    Article  ADS  Google Scholar 

  10. Y.Y. Yamaguchi, J. Barré, F. Bouchet, T. Dauxois, S. Ruffo, Physica A 337, 36 (2004)

    Article  ADS  Google Scholar 

  11. P.H. Chavanis, Ph.D. thesis, ENS Lyon (1996); P.H. Chavanis, J. Sommeria, R. Robert, Astroph. J. 471, 385 (1996)

  12. F. Hohl, J.W. Campbell, Collective motion of a one-dimensional self-gravitating system, NASA Technical Note TN D-5540, November (1969)

  13. T. Yamashiro, N. Gouda, M. Sakagami, Prog. Theor. Phys. 88, 269 (1992)

    Article  ADS  Google Scholar 

  14. M. Antoni, S. Ruffo, Phys. Rev. E 52, 2361 (1995)

    Article  ADS  Google Scholar 

  15. J. Barré, T. Dauxois, G. De Ninno, D. Fanelli, S. Ruffo, Phys. Rev. E 69, 045501 (2004)

    Article  ADS  Google Scholar 

  16. P.H. Chavanis, Eur. Phys. J. B 53, 487 (2006); A. Antoniazzi, D. Fanelli, J. Barré, P.-H. Chavanis, T. Dauxois, S. Ruffo, Phys. Rev. E 75, 011112 (2007)

    Article  ADS  Google Scholar 

  17. P. de Buyl, D. Mukamel, S. Ruffo, in Unsolved Problems of Noise and Fluctuations, AIP Conference Proceedings 800, 533 (2005)

    Article  ADS  Google Scholar 

  18. P.H. Chavanis, J. Vatteville, F. Bouchet, Eur. Phys. J. B 46, 61 (2005)

    Article  ADS  Google Scholar 

  19. W. Braun, K. Hepp, Comm. Math. Phys. 56, 101 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  20. A. Antoniazzi, F. Califano, D. Fanelli, S. Ruffo, Phys. Rev. Lett. 98, 150602 (2007)

    Article  ADS  Google Scholar 

  21. F. Baldovin, E. Orlandini, Phys. Rev. Lett. 96, 240602 (2006); F. Baldovin, E. Orlandini, Phys. Rev. Lett. 97, 100601 (2006)

    Article  ADS  Google Scholar 

  22. A. Campa, D. Mukamel, A. Giansanti, S. Ruffo, Phys. A 365, 120 (2006)

    Article  Google Scholar 

  23. F. Bouchet, T. Dauxois, Phys. Rev. E 72, 045103(R) (2005)

    Article  ADS  Google Scholar 

  24. P.H. Chavanis, Phys. A 361, 55 (2006); P.H. Chavanis, Phys. A 361, 81 (2006); doi:10.1016/j.physa.2007.10.026, doi:10.1016/j.physa.2007.10.034

    Article  MathSciNet  Google Scholar 

  25. V. Latora, A. Rapisarda, C. Tsallis, Phys. Rev. E 64, 056134 (2001); A. Pluchino, A Rapisarda, C. Tsallis, Europhys. Lett. 80, 26002 (2007)

    Article  ADS  Google Scholar 

  26. A. Antoniazzi, D. Fanelli, S. Ruffo, Y.Y. Yamaguchi, Phys. Rev. Lett. 99, 040601 (2007)

    Article  ADS  Google Scholar 

  27. F. Bouchet, T. Dauxois, D. Mukamel, S. Ruffo, Phase space gaps and ergodicity breaking in systems with long range interactions, e-print arXiv:0711.0268

  28. F. Borgonovi, G.L. Celardo, M. Maianti, E. Pedersoli, J. Stat. Phys. 116, 1435 (2004)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  29. W.B. Colson, Phys. Lett. A 59, 187 (1976); R. Bonifacio et al., Opt. Comm. 50, 373 (1984)

    Article  ADS  Google Scholar 

  30. J. Barré, F. Bouchet, T. Dauxois, S. Ruffo, J. Stat. Phys. 119, 677 (2005)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  31. Y. Elskens, D.F. Escande, Microscopic Dynamics of Plasmas and Chaos (IoP Publishing, Bristol, 2003)

    MATH  Google Scholar 

  32. A. Antoniazzi, G. De Ninno, D. Fanelli, A. Guarino, S. Ruffo, J. Phys.: Conf. Ser. 7, 143 (2005)

    Article  ADS  Google Scholar 

  33. A. Antoniazzi, R.S. Johal, D. Fanelli, S. Ruffo, Comm. Nonlin. Sci. Num. Simul. 13, 2 (2008)

    Article  MATH  ADS  Google Scholar 

  34. J. Barré, F. Bouchet, J. Stat. Phys. 118, 1073 (2005)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  35. C. von Cube et al., Phys. Rev. Lett. 93, 083601 (2004); C. von Cube et al., Fortschr. Phys. 54, 726 (2006)

    Article  ADS  Google Scholar 

  36. L.Q. English, M. Sato, A.J. Sievers, Phys. Rev. B 67, 024403 (2003)

    Article  ADS  Google Scholar 

  37. A. Campa, R. Khomeriki, D. Mukamel, S. Ruffo, Phys. Rev. B 76, 064415 (2007)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Energetica “S. Stecco” and CSDC, Università di Firenze, via s. Marta 3, 50139, Firenze, Italy

    S. Ruffo

  2. INFN, Sezione di Firenze, Firenze, Italy

    S. Ruffo

Authors
  1. S. Ruffo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Ruffo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ruffo, S. Equilibrium and nonequilibrium properties of systems with long-range interactions. Eur. Phys. J. B 64, 355–363 (2008). https://doi.org/10.1140/epjb/e2008-00044-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2008-00044-x

PACS

Search

Navigation