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Dynamical entropy of quasifree automorphisms. (English) Zbl 0628.46065

The dynamical entropy, as defined in: A. Connes, H. Narnhofer and W. Thirring, Commun. Math. Phys. 112, 691-719 (1987) is calculated for quasi free automorphisms and quasi free states and shown to be the entropy of the shift created by the group velocity.
Reviewer: G.Loupias

MSC:

46L55 Noncommutative dynamical systems
82B10 Quantum equilibrium statistical mechanics (general)
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References:

[1] Connes, A., Narnhofer, H., and Thirring, W., ?Dynamical Entropy of C*-Algebras and von Neumann Algebras?, submitted to Commun. Math. Phys. · Zbl 0637.46073
[2] KolmogorovA. N., Dokl. Akad. Nauk 119, 861 (1958).
[3] ConnesA. and StörmerE., Acta Math. 134, 289 (1975). · Zbl 0326.46032
[4] NarnhoferH., RequardtM., and ThirringW., Commun. Math. Phys. 92, 247 (1983). · Zbl 0534.46050
[5] Connes, A., Narnhofer, H., and Thirring, W., ?The Dynamical Entropy of Quantum Systems?, Lecture given at the Schladming Winter School 1987. · Zbl 0637.46073
[6] D’Antoni, C., Doplicher, S., Longo, R., and Fredenhagen, K., ?Convergence of Local Charges and Continuity Properties of W * Inclusions?, DESY 86-162. · Zbl 0657.46045
[7] ArakiH. and MatsuiT., Commun. Math. Phys. 101, 213 (1985); Lett. Math. Phys. 11, 87 (1986). · Zbl 0581.46058
[8] ThirringW., Lett. Math. Phys. 4, 67 (1980).
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