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Foundation of Entropy, Complexity and Fractals in Quantum Systems

  • Chapter
Probability Towards 2000

Part of the book series: Lecture Notes in Statistics ((LNS,volume 128))

Abstract

Fundamentals of quantum entropy are totally reviewed from von Neumann to recent works including new formulation of Kolmogorov-Sinai type dynamical entropy. Entropy is one of the most important quantities to describe a chaotic aspect of several different phenomena. There exist many trials to express the complexity of a dynamical system. I proposed Information Dynamics to synthesize the dynamics of state change and the complexity of system in 1991. In this paper, it is shown that the complexity of entropy type becomes a useful tool in the following two points: It generalizes the usual formulation of dynamical entropy so that it can be applied to concrete quantum processes like optical communication. New concept of fractal dimension, so-called the fractal dimension of a state, can be introduced by this entropic complexity.

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Author information

Authors and Affiliations

  1. Department of Information Sciences, Science University of Tokyo, Noda City, Chiba, 278, Japan

    Masanori Ohya

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  1. Masanori Ohya
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Editor information

Editors and Affiliations

  1. Centro Vito Volterra, Universita degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica, 00133, Roma, Italy

    L. Accardi

  2. Department of Statistics, Columbia University, 2990 Broadway Mail Code 4403, 10027, New York, NY, USA

    C. C. Heyde

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© 1998 Springer-Verlag New York, Inc.

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Ohya, M. (1998). Foundation of Entropy, Complexity and Fractals in Quantum Systems. In: Accardi, L., Heyde, C.C. (eds) Probability Towards 2000. Lecture Notes in Statistics, vol 128. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2224-8_16

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  • DOI: https://doi.org/10.1007/978-1-4612-2224-8_16

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98458-2

  • Online ISBN: 978-1-4612-2224-8

  • eBook Packages: Springer Book Archive

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