Skip to main content
SpringerLink
Log in

Fluctuation theorem and chaos

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

Abstract

The heat theorem (i.e. the second law of thermodynamics or the existence of entropy) is a manifestation of a general property of hamiltonian mechanics and of the ergodic hypothesis. In nonequilibrium thermodynamics of stationary states the chaotic hypothesis plays a similar role: it allows a unique determination of the probability distribution (called SRB distribution) on phase space providing the time averages of the observables. It also implies an expression for a few averages concrete enough to derive consequences of symmetry properties like the fluctuation theorem or to formulate a theory of coarse graining unifying the foundations of equilibrium and of nonequilibrium.

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. L. Boltzmann, Über die mechanische Bedeutung des zweiten Haupsatzes der Wärmetheorie, Wissenschaftliche Abhandlungen, edited by F. Hasenöhrl (Chelsea, New York, 1968), Vol. 1, p. 9

    Google Scholar 

  2. L. Boltzmann, Über die Eigenshaften monozyklischer und anderer damit verwandter Systeme, Wissenschaftliche Abhandlungen (Chelsea, New York, 1968), Vol. 3, p. 122

    Google Scholar 

  3. D.J. Evans, G.P. Morriss, Statistical Mechanics of Nonequilibrium Fluids (Academic Press, New York, 1990)

    Google Scholar 

  4. G. Gallavotti, Entropy, Chaos 16, 043114 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  5. D. Ruelle, Progress in Theoretical Physics Supplement 64, 339 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  6. D. Ruelle, Ergodic theory, Vol. Suppl X of The Boltzmann equation, edited by E.G.D Cohen, W. Thirring, Acta Physica Austriaca (Springer, New York, 1973)

    Google Scholar 

  7. G. Gallavotti, Eur. Phys. J. B 61, 1 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  8. G. Gallavotti, Annales de l’Institut H. Poincaré 70, 429 (1999) and chao-dyn/9703007

    MATH  MathSciNet  Google Scholar 

  9. G. Gallavotti, F. Bonetto, G. Gentile, Aspects of the ergodic, qualitative and statistical theory of motion (Springer Verlag, Berlin, 2004)

    MATH  Google Scholar 

  10. G. Gallavotti, E.G.D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)

    Article  ADS  Google Scholar 

  11. G. Gallavotti, Math. Phys. Elect. J. 1 1 (1995)

    MathSciNet  Google Scholar 

  12. G. Gallavotti, Open Syst. Inf. Dyn. 6, 101 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  13. G. Gallavotti, Statistical Mechanics. A short treatise (Springer Verlag, Berlin, 2000)

    Google Scholar 

  14. G. Gallavotti, Foundations of Fluid Dynamics, 2nd printing (Springer Verlag, Berlin, 2005)

    Google Scholar 

  15. G.N. Bochkov, Yu. E. Kuzovlev, Physica A 106, 443 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  16. G. Gentile, Forum Mathematicum 10, 89 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  17. F. Bonetto, G. Gallavotti, A. Giuliani, F. Zamponi, J. Stat. Phys. 123, 39 (2006)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  18. R. Van Zon, E.G.D. Cohen, Phys. Rev. Lett. 91, 110601, (2003)

    Article  Google Scholar 

  19. A. Giuliani, F. Zamponi, G. Gallavotti, J. Stat. Phys. 119, 944 (2005)

    Article  MathSciNet  Google Scholar 

  20. G. Gallavotti, Phys. Rev. Lett. 77, 4334 (1996)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  21. G. Gallavotti, D. Ruelle, Comm. Math. Phys. 190, 279 (1997)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. E.G.D. Cohen, G. Gallavotti, J. Stat. Phys. 96, 1343 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  23. M. Bandi, J.R. Cressman, W. Goldburg, J. Stat. Phys. 130, 27 (2008)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  24. F. Zamponi, J. Stat. Mech. P02008 (2007)

  25. G. Gallavotti, J. Stat. Phys. 78, 1571 (1995)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. G. Gallavotti, Comm. Math. Phys. 224, 107 (2001)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  27. G. Gallavotti, Chaos 16, 023130 (2006)

    ADS  Google Scholar 

  28. F. Bonetto, G. Gallavotti, A. Giuliani, F. Zamponi, J. Stat. Mech. P05009 (2006)

  29. G. Gallavotti, J. Stat. Mech. P10011 (2006)

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica and INFN, Università di Roma La Sapienza, P.A. Moro 2, 00185, Roma, Italy

    G. Gallavottia

Authors
  1. G. Gallavottia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Gallavottia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gallavottia, G. Fluctuation theorem and chaos. Eur. Phys. J. B 64, 315–320 (2008). https://doi.org/10.1140/epjb/e2008-00137-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2008-00137-6

PACS

Search

Navigation