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Quantum Entropy and Its Use : TEXTS AND MONOGRAPHS IN PHYSICS - Masanori Ohya

Quantum Entropy and Its Use

TEXTS AND MONOGRAPHS IN PHYSICS

Paperback

Published: 24th March 2004
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Entropy is a concept which appears in several fields and it is in the center of interest both in mathematical and physical subjects, sometimes even at other places, for example in communication engineering. The birthplace of quantum entropy was in quantum statistical mechanics. Quantum entropy is not a single concept but rather a family of notions which started with the von Neumann entropy of a density matrix and has developed in a number of directions. The heritage of quantum entropies from quantum mechanics is their strong relation to Hilbert space. This book begins with the entropy of a state and through the entropy of coarse graining it proceeds to the quantum dynamical entropy. A bunch of topics shows the direct physical relevance of the entropy methods. The math- ematical formalism is based on operator theory and mostly the language of operator algebras is used. The use of the concepts and methods of functional analysis not only makes the theory of quantum entropy more uniform and lu- cid, but it essentially simplifies and extends it. A comprehensive presentation without these elements would not be possible.

Entropies for finite quantum systems
Fundamental conceptsp. 15
Postulates for entropy and relative entropyp. 39
Convex trace functionsp. 49
Entropies for general quantum systems
Modular theory and auxiliariesp. 69
Relative entropy of states of operator algebrasp. 79
From relative entropy to entropyp. 101
Functionals of entropy typep. 113
Channeling transformation and coarse graining
Channels and their transposep. 137
Sufficient channels and measurementsp. 153
Dynamical entropyp. 175
Stationary processesp. 197
Perturbation theory
Perturbation of statesp. 215
Variational expression of perturbational limitsp. 231
Miscellanea
Central limit and quasi-free reductionp. 251
Thermodynamics of quantum spin systemsp. 269
Entropic uncertainty relationsp. 283
Temperley-Lieb algebras and indexp. 295
Optical communication processesp. 307
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540208068
ISBN-10: 3540208062
Series: TEXTS AND MONOGRAPHS IN PHYSICS
Audience: General
Format: Paperback
Language: English
Number Of Pages: 350
Published: 24th March 2004
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 22.86 x 15.24  x 1.91
Weight (kg): 0.54
Edition Number: 2