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© 2009

Quantum Entropies

Dynamics, Information and Complexity

Book

Part of the Theoretical and Mathematical Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Fabio Benatti
      Pages 1-4
  3. Classical Dynamical Systems

    1. Front Matter
      Pages 5-7
    2. Fabio Benatti
      Pages 9-69
    3. Fabio Benatti
      Pages 71-104
    4. Fabio Benatti
      Pages 105-134
  4. Quantum Dynamical Systems

    1. Front Matter
      Pages 135-137
    2. Fabio Benatti
      Pages 255-315
  5. Quantum Dynamical Entropies and Complexities

    1. Front Matter
      Pages 407-409
    2. Fabio Benatti
      Pages 411-481
    3. Fabio Benatti
      Pages 483-515
  6. Back Matter
    Pages 517-535

About this book

Introduction

The leading theme of the book is complexity in quantum dynamics. This issue is addressed by comparison with the classical ergodic, information and algorithmic complexity theories.

Of particular importance is the notion of Kolmogorov-Sinai dynamical entropy and of its inequivalent quantum extensions formulated by Connes, Narnhofer and Thirring on one hand and Alicki and Fannes on the other. Their connections with extensions to quantum systems of Kolmogorov-Chaitin-Solomonoff algorithmic complexity theory is also presented. The technical tools employed are those of the algebraic approach to quantum statistical mechanics which offers a unifying view of classical and quantum dynamical systems. Proofs and examples are provided in order to make the presentation self consistent.

Keywords

Algorithmic Complexity Quantum Computing Quantum Dynamical Entropies Quantum Dynamical Systems Quantum Entanglement Quantum Entropy Quantum Information Theory mechanics quantum mechanics

Authors and affiliations

  1. 1.Dipto. Fisica TeoricaUniversity of TriesteMiramareItaly

Bibliographic information

Reviews

From the reviews: “This book fits very well with the recent trends in theoretical and mathematical physics exploiting the interrelations between quantum theory, statistical mechanics and information theory. … The book is clearly written and contains a reasonable amount of elementary background material illustrated by numerous examples, and therefore can serve very well students at the graduate level and researchers entering the field of quantum dynamics and quantum information.” (Robert Alicki, Mathematical Reviews, Issue 2010 c)