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Dynamical entropy ofC* algebras and von Neumann algebras

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The definition of the dynamical entropy is extended for automorphism groups ofC* algebras. As an example, the dynamical entropy of the shift of a lattice algebra is studied, and it is shown that in some cases it coincides with the entropy density.

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References

  1. Kolmogorov, A.N.: Dokl. Akad. Nauk119, 861 (1958)

    Google Scholar 

  2. Sinai, Yu.: Dokl. Akad. Nauk124, 768 (1959)

    Google Scholar 

  3. Ruelle, D.: Thermodynamic formalism. Reading, Ma: Addison-Wesley 1978

    Google Scholar 

  4. Ruelle, D., Bowen, L.: Invent. Math.29, 181 (1975)

    Google Scholar 

  5. Lanford, O.E., Robinson, D.W.: Mean entropy states in quantum statistical mechanics. J. Math. Phys.9, 120 (1968)

    Google Scholar 

  6. Aizenman, M., Goldstein, S., Gruber, C., Lebowitz, J.L., Martin, P.: On the equivalence between KMS-states and equilibrium states for classical systems. Commun. Math. Phys.53, 209 (1977)

    Google Scholar 

  7. Lindblad, G.: Quantum ergodicity and chaos. In: Fundamental aspects of quantum theory, p. 199. Gorini, V., Frigerio, A. (eds.). New York: Plenum Press 1986

    Google Scholar 

  8. Lieb, E.H., Ruskai, M.B.: Proof of the strong subadditivity of quantum-mechanical entropy. J. Math. Phys.14, 1938 (1973)

    Google Scholar 

  9. Connes, A., Störmer, E.: Acat Math.134, 289 (1975)

    Google Scholar 

  10. Emch, G.: Acta Phys. Austr. [Suppl.]XV, 79 (1976)

    Google Scholar 

  11. Moore, S.M.: Rev. Colomb. Mat.X, 57 (1976)

    Google Scholar 

  12. Narnhofer, H., Thirring, W.: Fizika17, 257 (1985)

    Google Scholar 

  13. Connes, A.: C.R. Acad. Sci. Paris t301, I, 1 (1985)

    Google Scholar 

  14. Lieb, E.H.: Adv. Math.11, 267 (1973)

    Google Scholar 

  15. Araki, H.: Pub. Res. Inst. Math. Sci.9, 165 (1973)

    Google Scholar 

  16. Kosaki, H.: Interpolation theory and the Wigner-Yanase-Dyson-Lieb concavity. Commun. Math. Phys.87, 315 (1982)

    Google Scholar 

  17. Pusz, W., Woronowicz, S.: Form convex functions and the WYDL and other inequalities. Lett. Math. Phys.2, 505 (1978)

    Google Scholar 

  18. Choi, M.D., Effros, E.G.: Ann. Math.104, 585 (1976)

    Google Scholar 

  19. Choi, M.D., Effros, E.G.: J. Funct. Anal.24, 156 (1977)

    Google Scholar 

  20. Connes, A., Störmer, E.: J. Funct. Anal.28, 187 (1978)

    Google Scholar 

  21. Accardi, L., Cecchini, C.: Conditional expectations in von Neumann algebras and a theorem of Takesaki. J. Funct. Anal.45, 245–273 (1982)

    Google Scholar 

  22. Araki, H.: Gibbs states of a one dimensional quantum lattice. Commun. Math. Phys.14, 120 (1969)

    Google Scholar 

  23. Narnhofer, H.: Thermodynamical phases and surface effects. Acta Phys. Austr.54, 221 (1982)

    Google Scholar 

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Communicated by H. Araki

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Connes, A., Narnhofer, H. & Thirring, W. Dynamical entropy ofC* algebras and von Neumann algebras. Commun.Math. Phys. 112, 691–719 (1987). https://doi.org/10.1007/BF01225381

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  • DOI: https://doi.org/10.1007/BF01225381

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