Advertisement

Communications in Mathematical Physics

, Volume 35, Issue 4, pp 279–286 | Cite as

Gibbs processes and generalized Bernoulli flows for hard-core one-dimensional systems

  • G. Caldiera
  • E. Presutti
Article

Abstract

We consider a class of infinite-range potentials for which phase transitions are absent, and prove by the Ornstein-Friedman theorem, that they generate dynamical systems that are Bernoulli flows in a generalized sense.

Keywords

Neural Network Phase Transition Dynamical System Statistical Physic Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Gallavotti, G.: Ising model and Bernoulli schemes in one dimension. PreprintGoogle Scholar
  2. 2.
    Dobrushin, R.L.: Funkt. Analiz. Ego Pril.2, 31 (1968)Google Scholar
  3. 3.
    Ruelle, D.: Statistical mechanics of a one-dimensional lattice gas. Commun. math. Phys.9, 267 (1968)Google Scholar
  4. 4.
    Ornstein, D.S., Friedman, N.A.: On isomorphism of weakly Bernoulli transformation. Adv. Math.5, 365 (1971)Google Scholar
  5. 5.
    Gallavotti, G., Miracle-Sole, S.: A variational principle for the equilibrium of hard sphere systems. Ann. Inst. H. PoincaréVIII, 3, 287 (1968)Google Scholar
  6. 6.
    Gallavotti, G., Miracle-Sole, S.: Absence of phase-transitions in h.c. one-dimensional systems with long-range interactions. J. Math. Phys.11, 147 (1969)Google Scholar
  7. 7.
    Lanford, O.E., Ruelle, D.: Observables at infinity and states with short range correlations in statistical mechanics. Commun. math. Phys.13, 194 (1969)Google Scholar
  8. 8.
    Ornstein, D.: Two Bernoulli shifts with infinite entropy are isomorphic. Adv. Math.5, 339 (1971)Google Scholar
  9. 9.
    Ruelle, D.: Superstable interactions in classical statistical mechanics. Commun. math. Phys.18, 127 (1970)Google Scholar
  10. 10.
    Shields, P.C.: The theory of Bernoulli shifts. Notes.Google Scholar
  11. 11.
    Arnold, V.I., Avez, A.: Problemes ergodiques de la mecanique classique. Paris: Gauthier-Villars 1967Google Scholar
  12. 12.
    Robinson, D.W., Ruelle, D.: Mean entropy of states in classical statistical mechanics. Commun. math. Phys.5, 288 (1967)Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • G. Caldiera
    • 1
  • E. Presutti
    • 2
  1. 1.Istituto MatematicoUniversità di RomaRomaItaly
  2. 2.Istituto FisicoUniversità dell'AquilaL'AquilaItaly

Personalised recommendations