Quantum Entropies: Dynamics, Information and Complexity

Dr. Fabio Benatti (auth.)1402093055, 9781402093050, 9781402093067

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.

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Table of contents :
Front Matter….Pages I-XI
Front Matter….Pages 1-1
Introduction….Pages 1-4
Front Matter….Pages 5-7
Classical Dynamics and Ergodic Theory….Pages 9-69
Dynamical Entropy and Information….Pages 71-104
Algorithmic Complexity….Pages 105-134
Front Matter….Pages 135-137
Quantum Mechanics of Finite Degrees of Freedom….Pages 139-254
Quantum Information Theory….Pages 255-315
Quantum Mechanics of Infinite Degrees of Freedom….Pages 317-406
Front Matter….Pages 407-409
Quantum Dynamical Entropies….Pages 411-481
Quantum Algorithmic Complexities….Pages 483-515
Back Matter….Pages 517-535