Quantum Entropies Dynamics, Information and Complexity
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 entrop
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Theoretical and Mathematical Physics The series founded in 1975 and formerly (until 2005) entitled Texts and Monographs in Physics (TMP) publishes high-level monographs in theoretical and mathematical physics. The change of title to Theoretical and Mathematical Physics (TMP) signals that the series is a suitable publication platform for both the mathematical and the theoretical physicist. The wider scope of the series is reflected by the composition of the editorial board, comprising both physicists and mathematicians. The books, written in a didactic style and containing a certain amount of elementary background material, bridge the gap between advanced textbooks and research monographs. They can thus serve as basis for advanced studies, not only for lectures and seminars at graduate level, but also for scientists entering a field of research.
Editorial Board W. Beiglb¨ock, Institute of Applied Mathematics, University of Heidelberg, Germany J.-P. Eckmann, Department of Theoretical Physics, University of Geneva, Switzerland H. Grosse, Institute of Theoretical Physics, University of Vienna, Austria M. Loss, School of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA S. Smirnov, Mathematics Section, University of Geneva, Switzerland L. Takhtajan, Department of Mathematics, Stony Brook University, NY, USA J. Yngvason, Institute of Theoretical Physics, University of Vienna, Austria
For further volumes: http://www.springer.com/series/720
Fabio Benatti
Dynamics, Information and Complexity in Quantum Systems
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Dr. Fabio Benatti Universit`a Trieste Dipto. Fisica Teorica Strada Costiera, 11 34014 Trieste Miramare Italy [email protected]
ISBN 978-1-4020-9305-0
e-ISBN 978-1-4020-9306-7
DOI 10.1007/978-1-4020-9306-7 Library of Congress Control Number: 2008937916 c Springer Science+Business Media B.V. 2009 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com
To Heide, for her scholarship, for her friendship
Preface
The aim of this book is to offer a self-consistent overview of a series of issues relating entropy, information and dynamics in classical and quantum physics. My personal point of view regarding these matters is the result of what I had the good fortune to learn in the course of the years from various scientists: Heide Narnhofer in the first place, who introduced me to quantum dynamical entropies and was a precious guide ever since, then Robert Alicki, Mark Fannes, Giancarlo Ghirardi, Andreas Knauf, John Lewis, Geoffrey Sewell, Franco Strocchi, Walter Thirring, Armin Uhlmann. To me, all of them have been a constant example of rigorous mathematics and physical intuition jointly a
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