Communications in Mathematical Physics

, Volume 101, Issue 3, pp 363–382 | Cite as

Ergodic properties of a semi-infinite one-dimensional system of statistical mechanics

  • C. Boldrighini
  • A. Pellegrinotti
  • E. Presutti
  • Ya. G. Sinai
  • M. R. Soloveichik


We consider the dynamical system (\(\mathfrak{X}\),μ,T t ) where (\(\mathfrak{X}\),μ) is the Gibbs ensemble at some fixed temperature and density for a semi-infinite one-dimensional ideal gas of point particles. The first particle has massM, all the other particles massm<M. T t is the time evolution which describes free motion of the particles except for elastic collisions with each other and with the wall at the origin. We prove that (\(\mathfrak{X}\),μ,T t ) is aK-flow.


Neural Network Dynamical System Statistical Physic Complex System Time Evolution 
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  1. 1.
    Sinai, Ya. G., Volkoviiski, K.L.: Funct. Anal. Appl.5, 185–187 (1971)Google Scholar
  2. 2.
    Goldstein, S., Lebowitz, J.L., Aizenman, M.: Ergodic properties of infinite systems. In: Dynamical systems, theory, and application. Moser J., ed. Lecture Notes in Physics, Vol. 38, pp. 112–143. Berlin, Heidelberg, New York: Springer 1975Google Scholar
  3. 3.
    Goldstein, S., Lebowitz, J.L., Ravishankar, K.: Ergodic properties of a system in contact with a heat bath: a one dimensional model. Commun. Math. Phys.85, 419–427 (1982)Google Scholar
  4. 4.
    Landau, L.D., Lifschitz, E.M.: Statistical physics. New York: Pergamon 1969Google Scholar
  5. 5.
    Cornfeld, I.P., Fomin, S.V., Sinai, Ya.G.: Ergodic theory. Berlin, Heidelberg, New York: Springer 1982Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • C. Boldrighini
    • 1
  • A. Pellegrinotti
    • 2
  • E. Presutti
    • 3
  • Ya. G. Sinai
    • 4
  • M. R. Soloveichik
    • 5
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA
  2. 2.Dipartimento di MatematicaUniversità di CamerinoCamerinoItaly
  3. 3.Dipartimento di MatematicaUniversità La SapienzaRomaItaly
  4. 4.Landau Institute for Theoretical PhysicsMoscowUSSR
  5. 5.Moscow State UniversityMoscowUSSR

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