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

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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.

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References

  1. Gallavotti, G.: Ising model and Bernoulli schemes in one dimension. Preprint

  2. Dobrushin, R.L.: Funkt. Analiz. Ego Pril.2, 31 (1968)

    Google Scholar 

  3. Ruelle, D.: Statistical mechanics of a one-dimensional lattice gas. Commun. math. Phys.9, 267 (1968)

    Google Scholar 

  4. Ornstein, D.S., Friedman, N.A.: On isomorphism of weakly Bernoulli transformation. Adv. Math.5, 365 (1971)

    Google Scholar 

  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. 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. 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. Ornstein, D.: Two Bernoulli shifts with infinite entropy are isomorphic. Adv. Math.5, 339 (1971)

    Google Scholar 

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

    Google Scholar 

  10. Shields, P.C.: The theory of Bernoulli shifts. Notes.

  11. Arnold, V.I., Avez, A.: Problemes ergodiques de la mecanique classique. Paris: Gauthier-Villars 1967

    Google Scholar 

  12. Robinson, D.W., Ruelle, D.: Mean entropy of states in classical statistical mechanics. Commun. math. Phys.5, 288 (1967)

    Google Scholar 

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Authors and Affiliations

  1. Istituto Matematico, Università di Roma, Roma, Italy

    G. Caldiera

  2. Istituto Fisico, Università dell'Aquila, L'Aquila, Italy

    E. Presutti

Authors
  1. G. Caldiera
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  2. E. Presutti
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Research partially supported by the Consiglio Nazionale delle Ricerche (G.N.F.M.A.M.F.I.).

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Caldiera, G., Presutti, E. Gibbs processes and generalized Bernoulli flows for hard-core one-dimensional systems. Commun.Math. Phys. 35, 279–286 (1974). https://doi.org/10.1007/BF01646349

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  • DOI: https://doi.org/10.1007/BF01646349

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