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Communications in Mathematical Physics

, Volume 95, Issue 3, pp 301–305 | Cite as

Detailed balance and equilibrium

  • A. Verbeure
Article

Abstract

For classical lattice systems, an infinite set of jump-processes satisfying the condition of detailed balance is found. It is proved that any state invariant for these processes is an equilibrium state, providing a new characterization of DLR-states by means of the notion of detailed balance. This extends previous results, proved in one and two dimensions.

Keywords

Neural Network Statistical Physic Equilibrium State Complex System Nonlinear Dynamics 
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.

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References

  1. 1.
    Dobrushin, R.L.: Theory Probab. Appl.13, 197–224 (1968)Google Scholar
  2. 2.
    Lanford, O.E., Ruelle, D.: Observables at infinity and states with short range correlations in statistical mechanics. Commun. Math. Phys.13, 194–215 (1969)Google Scholar
  3. 3.
    Ruelle, D.: A variational formulation of equilibrium statistical mechanics and the Gibbs phase rule. Commun. Math. Phys.5, 324 (1967)Google Scholar
  4. 4.
    Fannes, M., Vanheuverzwijn, P., Verbeure, A.: Energy-entropy inequalities for classical lattice systems. J. Stat. Phys.29, 547–558 (1982)Google Scholar
  5. 5.
    Agarwal, G.S.: Open quantum Markovian systems and microreversibility. Z. Physik258, 409 (1973)Google Scholar
  6. 6.
    Carmichael, H.J., Walls, D.F.: Detailed balance in open quantum Markoffian systems. Z. Phys. B-Condensed Matter and Quanta23, 299 (1976)Google Scholar
  7. 7.
    Georgii, H.O.: Canonical Gibbs measures. In: Lecture Notes in Mathematics, Vol. 760. Berlin, Heidelberg, New York: Springer 1979Google Scholar
  8. 8.
    Sullivan, W.G.: Markov processes for Random fields. Comm. Dublin Institute for Advanced Studies. Series A, No. 23Google Scholar
  9. 9.
    Fannes, M., Verbeure, A.: On solvable models in classical lattice systems. Commun. Math. Phys. (to appear)Google Scholar
  10. 10.
    Quagebeur, J., Stragier, G., Verbeure, A.: Ann. Inst. H. Poincaré (to appear)Google Scholar
  11. 11.
    Kossakowski, A., Frigerio, A., Gorini, V., Verri, M.: Quantum detailed balance and KMS condition. Commun. Math. Phys.57, 97 (1977)Google Scholar
  12. 12.
    Robinson, D.W.: Statistical mechanics of quantum spin systems. II. Commun. Math. Phys.7, 337 (1968)Google Scholar
  13. 13.
    Liggett, Th. M.: Trans. Am. Math. Soc.165, 471 (1971)Google Scholar
  14. 14.
    Holley, R.A.: Free energy in a Markovian model of a lattice spin system. Commun. Math. Phys.23, 87 (1971)Google Scholar
  15. 15.
    Holley, R.A., Stroock, D.W.: In one and two dimensions, every stationary measure for a stochastic Ising model is a Gibbs state. Commun. Math. Phys.55, 37 (1977)Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • A. Verbeure
    • 1
  1. 1.Instituut voor Theoretische NatuurkundeUniversiteit LeuvenLeuvenBelgium

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