Skip to main content
SpringerLink
Log in

Adiabatic Piston as a Dynamical System

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

Abstract

We consider systems of finitely many interacting particles in a cube with a separating wall having a big mass M(adiabatic piston). Assuming that the particles reflect elastically from the ball and the initial velocity of the piston is zero we prove that as Mtends to infinity the dynamics of the piston converges to periodic oscillations.

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. D. V. Anosov, Averaging in systems of ordinary differential equations with rapidly oscillating solutions, Izv. Akad. Nauk SSSR, Ser. Mat. 24:721–742 (1960).

    Google Scholar 

  2. V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations(Springer-Verlag, 1983), p. 334.

  3. N. I. Chernov, J. L. Lebowitz, and Y. G. Sinai, Dynamics of a massive piston in an ideal gas, Russian Math. Surveys 57:1045–1125 (2002).

    Google Scholar 

  4. C. Gruber, Thermodynamics of systems with internal adiabatic constraints: Time evolution of the adiabatic piston, European J. Phys. 20:259–266 (1999).

    Google Scholar 

  5. Hard Ball Systems and Lorentz Gas, Encyclopaedia Math. Sci., Vol. 101 (Springer-Verlag, 2000).

  6. T. Kasuga, On the adiabatic theorem for the Hamiltonian system of differential equations in classical mechanics. I, II, III, Proc. Japan Acad. 37:366–382 (1961).

    Google Scholar 

  7. E. Lieb, Some problems in statistical mechanics that I would like to see solved, Phys. A 263:491–499 (1999).

    Google Scholar 

  8. J. L. Lebowitz, J. Piasecki, and Y. G. Sinai, Scaling dynamics of a massive piston in an ideal gas, in Hard Ball Systems and Lorentz Gas, Encyclopaedia Math. Sci., Vol. 101 (Springer-Verlag, 2000), pp. 217–227.

    Google Scholar 

  9. Y. G. Sinai, Dynamics of a massive particle surrounded by a finite number of light particles, Theor. Math. Phys. 125:1351–1357 (1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Space Research Institute, Russian Academy of Sciences, Russia

    A. I. Neishtadt

  2. Mathematics Department, Princeton University, USA

    Y. G. Sinai

  3. Landau Institute of Theoretical Physics, Russian Academy of Sciences, Russia

    Y. G. Sinai

Authors
  1. A. I. Neishtadt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. G. Sinai
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Neishtadt, A.I., Sinai, Y.G. Adiabatic Piston as a Dynamical System. Journal of Statistical Physics 116, 815–820 (2004). https://doi.org/10.1023/B:JOSS.0000037222.64432.62

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JOSS.0000037222.64432.62

Search

Navigation