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Theoretical and Mathematical Physics

By: M. Ohya, Denes Petz

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Paperback | 24 March 2004 | Edition Number 2

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364 Pages

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22.86 x 15.24 x 1.91

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This monograph, by now a standard reference in the field, provides a complete overview of quantum entropy theory, from the early days of quantum mechanics up to the most recent developments. It employs mathematical formalism based on operator theory and functional analysis with a goal of creating a comprehensive account of the different entropy concepts, their interrelations and use. Among the ideas discussed are entropy of a quantum state, relative entropy, mutual entropy, entropy of a coarse graining and dynamical entropy. Numerous fundamental properties of quantum information measurement are developed, including the von Neumann entropy of a statistical operator and its limiting normalized version, the entropy rate. Use of quantum-entropy quantities is made in perturbation theory, central limit theorems, thermodynamics of spin systems, entropic uncertainty relations, and optical communication. This new softcover corrected reprint contains summaries of recent developments added to the ends of the chapters.

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Entropies for finite quantum systems
Fundamental concepts	p. 15
Postulates for entropy and relative entropy	p. 39
Convex trace functions	p. 49
Entropies for general quantum systems
Modular theory and auxiliaries	p. 69
Relative entropy of states of operator algebras	p. 79
From relative entropy to entropy	p. 101
Functionals of entropy type	p. 113
Channeling transformation and coarse graining
Channels and their transpose	p. 137
Sufficient channels and measurements	p. 153
Dynamical entropy	p. 175
Stationary processes	p. 197
Perturbation theory
Perturbation of states	p. 215
Variational expression of perturbational limits	p. 231
Miscellanea
Central limit and quasi-free reduction	p. 251
Thermodynamics of quantum spin systems	p. 269
Entropic uncertainty relations	p. 283
Temperley-Lieb algebras and index	p. 295
Optical communication processes	p. 307
Table of Contents provided by Blackwell. All Rights Reserved.

Theoretical and Mathematical Physics

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Condensed Matter Physics including Liquid State & Solid State Physics

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Thermodynamics and Kinetics of Materials

Engineering Materials

Solid State Physics

Computational Physics II

Simulation of Classical and Quantum Systems

Polymer Physics Disentangled

An Introduction for Scientists and Engineers

Structures on Different Time Scales

Volume 2

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