Statistical Mechanics
Third Edition
,Statistical Mechanics
Third Edition
R. K. Pathria
Department of Physics
University of California at San Diego
Paul D. Beale
Department of Physics
University of Colorado at Boulder
AMSTERDAM • BOSTON • HEIDELBERG • LONDON
NEW YORK • OXFORD • PARIS • SAN DIEGO
SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO
Butterworth-Heinemann is an imprint of Elsevier
,Butterworth-Heinemann is an imprint of Elsevier
The Boulevard, Langford Lane, Kidlington, Oxford, 0X5 1GB, UK
30 Corporate Drive, Suite 400, Burlington, MA 01803, USA
First published 1972; Second edition 1996
© 2011 Elsevier Ltd. All rights reserved
The right of R. K. Pathria to be identified as the author of this work has been asserted in accordance with the Copyright, Designs
and Patents Act 1988.
No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including
photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements
with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our
website: www.elsevier.com/permissions.
This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as
may be noted herein).
Notices
Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding,
changes in research methods, professional practices, or medical treatment may become necessary.
Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any
information, methods, compounds, or experiments described herein. In using such information or methods they should be
mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.
To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any
injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or
operation of any methods, products, instructions, or ideas contained in the material herein.
British Library Cataloguing in Publication Data
A catalogue of this book is available from the British Library.
Library of Congress Cataloging in Publication Data
Pathria, R. K.
Statistical mechanics–3rd ed. / R. K. Pathria, Paul D. Beale.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-12-382188-1 (pbk.)
1. Statistical mechanics. I. Beale, Paul D. II. Title.
QC174.8.P38 2011
530.13–dc22 2010048955
Cover: The image was created using the opensource software CMBview (http://www.jportsmouth.com/code/CMBview/
cmbview.html) written by Jamie Portsmouth and used with permission. It was created using the WMAP seven-year Internal
Linear Combination Map courtesy of the WMAP Science Team (http://lambda.gsfc.nasa.gov/product/map/dr4/ilc map get.cfm).
For information on all Butterworth-Heinemann publications,
visit our Web site at www.elsevierdirect.com
Printed in the United States
11 12 13 14 15 10 9 8 7 6 5 4 3 2 1
, Preface to the Third Edition
The second edition of Statistical Mechanics was published in 1996. The new material added at
that time focused on phase transitions, critical phenomena, and the renormalization group —
topics that had undergone vast transformations during the years following the publication of
the first edition in 1972. In 2009, R. K. Pathria (R.K.P.) and the publishers agreed it was time for
a third edition to incorporate the important changes that had occurred in the field since the
publication of the second edition and invited Paul B. Beale (P.D.B.) to join as coauthor. The two
authors agreed on the scope of the additions and changes and P.D.B. wrote the first draft of
the new sections except for Appendix F which was written by R.K.P. Both authors worked very
closely together editing the drafts and finalizing this third edition.
The new topics added to this edition are:
. Bose–Einstein condensation and degenerate Fermi gas behavior in ultracold atomic gases:
Sections 7.2, 8.4, 11.2.A, and 11.9. The creation of Bose–Einstein condensates in ultracold
gases during the 1990s and in degenerate Fermi gases during the 2000s led to a revolution
in atomic, molecular, and optical physics, and provided a valuable link to the quantum
behavior of condensed matter systems. Several of P.D.B.’s friends and colleagues in physics
. and JILA at the University of Colorado have been leaders in this exciting new field.
Finite-size scaling behavior of Bose–Einstein condensates: Appendix F. We develop an
analytical theory for the behavior of Bose–Einstein condensates in a finite system, which
provides a rigorous justification for singling out the ground state in the calculation of the
. properties of the Bose–Einstein condensate.
Thermodynamics of the early universe: Chapter 9. The sequence of thermodynamic
transitions that the universe went though shortly after the Big Bang left behind mileposts
that astrophysicists have exploited to look back into the universe’s earliest moments. Major
advances in astronomy over the past 20 years have provided a vast body of observational
data about the early evolution of the universe. These include the Hubble Space Telescope’s
deep space measurements of the expansion of the universe, the Cosmic Background
Explorer’s precise measurements of the temperature of the cosmic microwave background,
and the Wilkinson Microwave Anisotropy Probe’s mapping of the angular variations in the
cosmic microwave background. These data sets have led to precise determinations of the
age of the universe, its composition and early evolution. Coincidentally, P.D.B.’s faculty
office is located in the tower named after George Gamow, a member of the faculty at the
University of Colorado in the 1950s and 1960s and a leader in the theory of nucleosynthesis
. in the early universe.
Chemical equilibrium: Section 6.6. Chemical potentials determine the conditions
necessary for chemical equilibrium. This is an important topic in its own right, but also
plays a critical role in our discussion of the thermodynamics of the early universe in
Chapter 9.
xiii
Third Edition
,Statistical Mechanics
Third Edition
R. K. Pathria
Department of Physics
University of California at San Diego
Paul D. Beale
Department of Physics
University of Colorado at Boulder
AMSTERDAM • BOSTON • HEIDELBERG • LONDON
NEW YORK • OXFORD • PARIS • SAN DIEGO
SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO
Butterworth-Heinemann is an imprint of Elsevier
,Butterworth-Heinemann is an imprint of Elsevier
The Boulevard, Langford Lane, Kidlington, Oxford, 0X5 1GB, UK
30 Corporate Drive, Suite 400, Burlington, MA 01803, USA
First published 1972; Second edition 1996
© 2011 Elsevier Ltd. All rights reserved
The right of R. K. Pathria to be identified as the author of this work has been asserted in accordance with the Copyright, Designs
and Patents Act 1988.
No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including
photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements
with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our
website: www.elsevier.com/permissions.
This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as
may be noted herein).
Notices
Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding,
changes in research methods, professional practices, or medical treatment may become necessary.
Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any
information, methods, compounds, or experiments described herein. In using such information or methods they should be
mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.
To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any
injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or
operation of any methods, products, instructions, or ideas contained in the material herein.
British Library Cataloguing in Publication Data
A catalogue of this book is available from the British Library.
Library of Congress Cataloging in Publication Data
Pathria, R. K.
Statistical mechanics–3rd ed. / R. K. Pathria, Paul D. Beale.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-12-382188-1 (pbk.)
1. Statistical mechanics. I. Beale, Paul D. II. Title.
QC174.8.P38 2011
530.13–dc22 2010048955
Cover: The image was created using the opensource software CMBview (http://www.jportsmouth.com/code/CMBview/
cmbview.html) written by Jamie Portsmouth and used with permission. It was created using the WMAP seven-year Internal
Linear Combination Map courtesy of the WMAP Science Team (http://lambda.gsfc.nasa.gov/product/map/dr4/ilc map get.cfm).
For information on all Butterworth-Heinemann publications,
visit our Web site at www.elsevierdirect.com
Printed in the United States
11 12 13 14 15 10 9 8 7 6 5 4 3 2 1
, Preface to the Third Edition
The second edition of Statistical Mechanics was published in 1996. The new material added at
that time focused on phase transitions, critical phenomena, and the renormalization group —
topics that had undergone vast transformations during the years following the publication of
the first edition in 1972. In 2009, R. K. Pathria (R.K.P.) and the publishers agreed it was time for
a third edition to incorporate the important changes that had occurred in the field since the
publication of the second edition and invited Paul B. Beale (P.D.B.) to join as coauthor. The two
authors agreed on the scope of the additions and changes and P.D.B. wrote the first draft of
the new sections except for Appendix F which was written by R.K.P. Both authors worked very
closely together editing the drafts and finalizing this third edition.
The new topics added to this edition are:
. Bose–Einstein condensation and degenerate Fermi gas behavior in ultracold atomic gases:
Sections 7.2, 8.4, 11.2.A, and 11.9. The creation of Bose–Einstein condensates in ultracold
gases during the 1990s and in degenerate Fermi gases during the 2000s led to a revolution
in atomic, molecular, and optical physics, and provided a valuable link to the quantum
behavior of condensed matter systems. Several of P.D.B.’s friends and colleagues in physics
. and JILA at the University of Colorado have been leaders in this exciting new field.
Finite-size scaling behavior of Bose–Einstein condensates: Appendix F. We develop an
analytical theory for the behavior of Bose–Einstein condensates in a finite system, which
provides a rigorous justification for singling out the ground state in the calculation of the
. properties of the Bose–Einstein condensate.
Thermodynamics of the early universe: Chapter 9. The sequence of thermodynamic
transitions that the universe went though shortly after the Big Bang left behind mileposts
that astrophysicists have exploited to look back into the universe’s earliest moments. Major
advances in astronomy over the past 20 years have provided a vast body of observational
data about the early evolution of the universe. These include the Hubble Space Telescope’s
deep space measurements of the expansion of the universe, the Cosmic Background
Explorer’s precise measurements of the temperature of the cosmic microwave background,
and the Wilkinson Microwave Anisotropy Probe’s mapping of the angular variations in the
cosmic microwave background. These data sets have led to precise determinations of the
age of the universe, its composition and early evolution. Coincidentally, P.D.B.’s faculty
office is located in the tower named after George Gamow, a member of the faculty at the
University of Colorado in the 1950s and 1960s and a leader in the theory of nucleosynthesis
. in the early universe.
Chemical equilibrium: Section 6.6. Chemical potentials determine the conditions
necessary for chemical equilibrium. This is an important topic in its own right, but also
plays a critical role in our discussion of the thermodynamics of the early universe in
Chapter 9.
xiii
