Statistical Physics. An introduction - D.Yoshioka, Springer, 2007.pdf

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Statistical Physics
Daijiro Yoshioka
Statistical
Physics
An Introduction
With 71 Figures and 7 Tables
123
Professor Daijiro Yoshioka
Department of Basic Science
The University of Tokyo
3-8-1 Komaba, Meguro
Tokyo, 153-8902
Japan
e-mail: daijiro@toki.c.u-tokyo.ac.jp
ISBN-10 3-540-28605-5 Springer Berlin Heidelberg New York
ISBN-13 978-3-540-28605-9 Springer Berlin Heidelberg New York
Library of Congress Control Number: 2006923850
This work is subject to copyright. All rights are reserved, whether the whole or part
of the material is concerned, specif ically the rights of translation, reprinting, reuse
of illustrations, recitation, broadcasting, reproduction onmicrof ilm or in any other
way, and storage in data banks. Duplication of this publication or parts thereof is
permitted only 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. Violations are liable to prosecution under the German Copyright Law.
Springer is part of Springer Science+Business Media
springer.com
© Springer-Verlag Berlin Heidelberg 2007
The use of general descriptive names, registered names, trademarks, etc. in this
publication does not imply, even in the absence of a specif ic statement, that such
names are exempt from the relevant protective laws and regulations and therefore
free for general use.
Production and Typesetting: LE-T E X Jelonek, Schmidt & Vöckler GbR, Leipzig
Cover design: WMX Design GmbH, Heidelberg
SPIN 10963821
57/3100YL - 5 4 3 2 1 0 Printed on acid-free paper
Preface
“More is different” is a famous aphorism of P.W. Anderson, who contributed
rather a lot to the development of condensed-matter physics in the latter
half of the 20th century. He claimed, by this aphorism, that macroscopic sys-
tems behave in a way that is qualitatively different from microscopic systems.
Therefore, additional rules are needed to understand macroscopic systems,
rules additional to the fundamental laws for individual atoms and molecules.
An example is provided by the various kinds of phase transitions that occur.
The state of a sample of matter changes drastically at a transition, and sin-
gular behavior is observed at the transition point. Another good example in
which quantity brings about a qualitative difference is the brain. A brain con-
sists of a macroscopic number of neural cells. It is believed that every brain
cell functions like an element of a computer. However, even the most sophis-
ticated computer consists of only a limited number of elements and has no
consciousness. The study of the human brain is still developing.
On the other hand, the paradigm for macroscopic matter, namely thermo-
dynamics and statistical physics, has a long history of investigation. The first
and second laws of thermodynamics and the principle of equal probability in
statistical physics have been established as laws that govern systems consisting
of a macroscopic number of molecules, such as liquids, gases, and solids (met-
als, semiconductors, insulators, magnetic materials, etc.). These laws belong
to a different hierarchy from the laws at the microscopic level, and cannot be
deduced from the latter laws, i.e. quantum mechanics and the laws for forces.
Therefore, a “theory of everything” is useless without these thermodynamic
and statistical-mechanical laws in the real world. The purpose of this book is
to explain these laws of the macroscopic level to undergraduate students who
are learning statistical physics for the first time.
In this book, we start from a description of a macroscopic system. We
then investigate ideal gases kinematically. Following on from the discussion
of the results, we introduce the principle of equal probability. In the second
and third chapters we explain the general principles of statistical physics on
the basis of this principle. We start our discussion by defining entropy. Then

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