A Fundamental Property of Quantum-Mechanical Entropy
There are some properties of entropy, such as concavity and subadditivity, that are known to hold (in classical and in quantum mechanics) irrespective of any assumptions on the detailed dynamics of a system. These properties are consequences of the defini
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Springer-Verlag Berlin Heidelberg GmbH
ELLIOTT H. LIEB
Inequalities Selecta of Elliott H. Lieb
Edited by M. Loss and M.B. Ruskai
Springer
Professor Elliott H. Lieb Jadwin Hall Departments of Mathematics and Physics Princeton University P.O. Box 708
Princeton, New Jersey 08544-0708, USA
Professor Michael Loss School of Mathematics Georgia Tech Atlanta, GA 30332-0160, USA
Professor Mary Beth Ruskai Department of Mathematics University of Massachusetts Lowell Lowell, MA 01854, USA
Library of Congress Cataloging-in-Publication Data Lieb, Elliott H. Inequalities : selecta of Elliott H. Lieb / edited by M. Loss and M.B. Ruskai. p. cm. Includes bibliographical references. ISBN 978-3-642-62758-3 ISBN 978-3-642-55925-9 (eBook) DOI 10.1007/978-3-642-55925-9
1. Inequalities (Mathematics) 1. Loss, 1954-II. Ruskai, Mary Beth. III. Title. QA295 .L54 2002 515'.26--dc21 2002021784 QC173.4.T48 L54 2001 539'.1-dc21 2001041096
First Edition 2002. Corrected Second Printing 2003 ISBN 978-3-642-62758-3 This work is subject to copyright. AlI rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted on1y under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag.Violations are liable for prosecution under the German Copyright Law.
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Softcover reprint of the hardcover
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edition 2002
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SPIN 10911358
55/3141/XO - 5 4 3 2 1 o
Preface
Elliott Lieb made seminal contributions to physics and mathematics. The former are partially collected in the volume "The Stability of Matter: From Atoms to Stars" (Selecta of Elliott Lieb), now in its third edition, which contains some of his papers on the structure of matter, such as its stability and the existence of thermodynamic functions. This new volume is a selection of his contributions to analysis, in particular his work on inequalities. There are several reasons for publishing this collection of his work. Many of Lieb's results have a substantial impact on analysis, such as his work with Brascamp that determined the sharp constant in Young's inequality. Another example is his work with various collaborators on rearrangement inequalities, which is an area now fully recognized as a very valuable part of analysis. A second important consideration is the long shelflife ofLieb's work. For example, the paper 'Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture' (No 11
