Skip to main content
SpringerLink
Log in

Frictionless Thermostats and Intensive Constants of Motion

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Thermostats models in space dimension d=1,2,3 for nonequilibrium statistical mechanics are considered and it is shown that, in the thermodynamic limit, the evolutions admit infinitely many constants of motion: namely the intensive observables.

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. Feynman, R.P., Vernon, F.L.: The theory of a general quantum system interacting with a linear dissipative system. Ann. Phys. 24, 118–173 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  2. Marchioro, C., Pellegrinotti, A., Presutti, E.: Existence of time evolution for ν dimensional statistical mechanics. Commun. Math. Phys. 40, 175–185 (1975)

    Article  MathSciNet  ADS  Google Scholar 

  3. Ruelle, D.: Statistical Mechanics. Benjamin, New York (1969)

    MATH  Google Scholar 

  4. Lanford, O., Ruelle, D.: Observables at infinity and states with short range correlations in statistical mechanics. Commun. Math. Phys. 13, 194–215 (1969)

    Article  MathSciNet  ADS  Google Scholar 

  5. Gentile, G., Procesi, M.: Periodic solutions for a class of nonlinear partial differential equations in higher dimension. Commun. Math. Phys. 289, 863–906 (2009)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. Gallavotti, G., Presutti, E.: Nonequilibrium, thermostats and thermodynamic limit. J. Math. Phys. 51, 015202 (2010)

    Article  ADS  Google Scholar 

  7. Gallavotti, G., Miracle-Solé, S.: Statistical mechanics of lattice systems. Commun. Math. Phys. 5, 317–323 (1967)

    Article  MATH  ADS  Google Scholar 

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

    MATH  Google Scholar 

  9. Ruelle, D.: Superstable interactions in classical statistical mechanics. Commun. Math. Phys. 18, 127–159 (1970)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. Fritz, J., Dobrushin, R.L.: Non-equilibrium dynamics of two-dimensional infinite particle systems with a singular interaction. Commun. Math. Phys. 57, 67–81 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  11. Caglioti, E., Marchioro, C., Pulvirenti, M.: Non-equilibrium dynamics of three-dimensional infinite particle systems. Commun. Math. Phys. 215, 25–43 (2000)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. Sinai, Ya.G.: Construction of dynamics in one-dimensional systems of statistical mechanics. Theor. Math. Phys. 11, 487–494 (1972)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  14. Gallavotti, G.: On thermostats: Isokinetic or Hamiltonian? Finite or infinite? Chaos 19, 013101 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  15. Williams, S.R., Searles, D.J., Evans, D.J.: Independence of the transient fluctuation theorem to thermostatting details. Phys. Rev. E 70, 066113 (2004)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fisica-INFN, Università di Roma 1, Roma, Italy

    G. Gallavotti

  2. Matematica, Università di Roma 2, Roma, Italy

    E. Presutti

Authors
  1. G. Gallavotti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Presutti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Gallavotti.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gallavotti, G., Presutti, E. Frictionless Thermostats and Intensive Constants of Motion. J Stat Phys 139, 618–629 (2010). https://doi.org/10.1007/s10955-010-9949-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-010-9949-0

Keywords

Search

Navigation