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- Herausgeber: Wiley-VCH Verlag GmbH & Co. KGaA
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
A Modern Course in Statistical Physics is a textbook that illustrates the foundations of equilibrium and non-equilibrium statistical physics, and the universal nature of thermodynamic processes, from the point of view of contemporary research problems.
The book treats such diverse topics as the microscopic theory of critical phenomena, superfluid dynamics, quantum conductance, light scattering, transport processes, and dissipative structures, all in the framework of the foundations of statistical physics and thermodynamics. It shows the quantum origins of problems in classical statistical physics. One focus of the book is fluctuations that occur due to the discrete nature of matter, a topic of growing importance for nanometer scale physics and biophysics. Another focus concerns classical and quantum phase transitions, in both monatomic and mixed particle systems.
This fourth edition extends the range of topics considered to include, for example, entropic forces, electrochemical processes in biological systems and batteries, adsorption processes in biological systems, diamagnetism, the theory of Bose-Einstein condensation, memory effects in Brownian motion, the hydrodynamics of binary mixtures.
A set of exercises and problems is to be found at the end of each chapter and, in addition, solutions to a subset of the problems is provided. The appendices cover Exact Differentials, Ergodicity, Number Representation, Scattering Theory, and also a short course on Probability.
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Veröffentlichungsjahr: 2016
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Table of Contents
Cover
Title
Author
Copyright
Preface to the Fourth Edition
1 Introduction
2 Complexity and Entropy
2.1 Introduction
2.2 Counting Microscopic States
2.3 Probability
2.4 Multiplicity and Entropy of Macroscopic Physical States
2.5 Multiplicity and Entropy of a Spin System
2.6 Entropic Tension in a Polymer
2.7 Multiplicity and Entropy of an Einstein Solid
2.8 Multiplicity and Entropy of an Ideal Gas
2.9 Problems
3 Thermodynamics
3.1 Introduction
3.2 Energy Conservation
3.3 Entropy
3.4 Fundamental Equation of Thermodynamics
3.5 Thermodynamic Potentials
3.6 Response Functions
3.7 Stability of the Equilibrium State
3.8 Cooling and Liquefaction of Gases
3.9 Osmotic Pressure in Dilute Solutions
3.10 The Thermodynamics of Chemical Reactions
3.11 The Thermodynamics of Electrolytes
3.12 Problems
4 The Thermodynamics of Phase Transitions
4.1 Introduction
4.2 Coexistence of Phases: Gibbs Phase Rule
4.3 Classification of Phase Transitions
4.4 Classical Pure PVT Systems
4.5 Binary Mixtures
4.6 The Helium Liquids
4.7 Superconductors
4.8 Ginzburg–Landau Theory
4.9 Critical Exponents
4.10 Problems
5 EquilibriumStatistical Mechanics I – Canonical Ensemble
5.1 Introduction
5.2 Probability Density Operator – Canonical Ensemble
5.3 Semiclassical Ideal Gas of Indistinguishable Particles
5.4 Interacting Classical Fluids
5.5 Heat Capacity of a Debye Solid
5.6 Order–Disorder Transitions on Spin Lattices
5.7 Scaling
5.8 Microscopic Calculation of Critical Exponents
5.9 Problems
6 EquilibriumStatistical Mechanics II – Grand Canonical Ensemble
6.1 Introduction
6.2 The Grand Canonical Ensemble
6.3 Adsorption Isotherms
6.4 Virial Expansion for Interacting Classical Fluids
6.5 Blackbody Radiation
6.6 Ideal Quantum Gases
6.7 Ideal Bose–Einstein Gas
6.8 BogoliubovMean Field Theory
6.9 Ideal Fermi–Dirac Gas
6.10 Magnetic Susceptibility of an Ideal Fermi Gas
6.11 Momentum Condensation in an Interacting Fermi Fluid
6.12 Problems
7 Brownian Motion and Fluctuation–Dissipation
7.1 Introduction
7.2 BrownianMotion
7.3 The Fokker–Planck Equation
7.4 Dynamic Equilibrium Fluctuations
7.5 Linear Response Theory and the Fluctuation–Dissipation Theorem
7.6 Microscopic Linear Response Theory
7.7 Thermal Noise in the Electron Current
7.8 Problems
8 Hydrodynamics
8.1 Introduction
8.2 Navier–StokesHydrodynamic Equations
8.3 Linearized Hydrodynamic Equations
8.4 Light Scattering
8.5 Friction on a Brownian particle
8.6 BrownianMotion withMemory
8.7 Hydrodynamics of Binary Mixtures
8.8 Thermoelectricity
8.9 Superfluid Hydrodynamics
8.10 Problems
9 Transport Coefficients
9.1 Introduction
9.2 Elementary Transport Theory
9.3 The Boltzmann Equation
9.4 Linearized Boltzmann Equations for Mixtures
9.5 Coefficient of Self-Diffusion
9.6 Coefficients of Viscosity and Thermal Conductivity
9.7 Computation of Transport Coefficients
9.8 Beyond the Boltzmann Equation
9.9 Problems
10 Nonequilibrium Phase Transitions
10.1 Introduction
10.2 Near Equilibrium Stability Criteria
10.3 The Chemically Reacting Systems
10.4 The Rayleigh–Bénard Instability
10.5 Problems
Appendix A: Probability and Stochastic Processes
A.1 Probability
A.2 Stochastic Processes
A.3 Problems
Appendix B: Exact Differentials
Appendix C: Ergodicity
Appendix D: Number Representation
D.1 Symmetrized and Antisymmetrized States
D.2 The Number Representation
Appendix E: Scattering Theory
E.1 Classical Dynamics of the Scattering Process
E.2 The Scattering Cross Section
E.3 Quantum Dynamics of Low-Energy Scattering
Appendix F: Useful Math and Problem Solutions
F.1 Useful Mathematics
F.2 Solutions for Odd-Numbered Problems
References
Index
End User License Agreement
Guide
Cover
Table of Contents
Begin Reading
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Linda E. Reichl
A Modern Course in Statistical Physics
4th revised and updated edition
Author
Linda E. Reichl
University of Texas
Center for Complex Quantum Systems
Austin, TX 78712
USA
Cover
Bose–Einstein condensates;
courtesy of Daniel J. Heinzen
All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Library of Congress Card No.:
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British Library Cataloguing-in-Publication Data:
A catalogue record for this book is available from the British Library.
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The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de.
© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Print ISBN 978-3-527-41349-2
ePDF ISBN 978-3-527-69046-6
ePub ISBN 978-3-527-69048-0
Mobi ISBN 978-3-527-69047-3
oBook ISBN 978-3-527-69049-7
Preface to the Fourth Edition
A Modern Course in Statistical Physics has gone through several editions. The first edition was published in 1980 by University of Texas Press. It was well received because it contained a presentation of statistical physics that synthesized the best of the american and european “schools” of statistical physics at that time. In 1997, the rights to A Modern Course in Statistical Physics were transferred to John Wiley & Sons and the second edition was published. The second edition was a much expanded version of the first edition, and as we subsequently realized, was too long to be used easily as a textbook although it served as a great reference on statistical physics. In 2004, Wiley-VCH Verlag assumed rights to the second edition, and in 2007 we decided to produce a shortened edition (the third) that was explicitly written as a textbook. The third edition appeared in 2009.
Statistical physics is a fast moving subject and many new developments have occurred in the last ten years. Therefore, in order to keep the book “modern”, we decided that it was time to adjust the focus of the book to include more applications in biology, chemistry and condensed matter physics. The core material of the book has not changed, so previous editions are still extremely useful. However, the new fourth edition, which is slightly longer than the third edition, changes some of its focus to resonate with modern research topics.
The first edition acknowledged the support and encouragement of Ilya Prigogine, who directed the Center for Statistical Mechanics at the U.T. Austin from 1968 to 2003. He had an incredible depth of knowledge in many fields of science and helped make U.T. Austin an exciting place to be. The second edition was dedicated to Ilya Prigogine “for his encouragement and support, and because he has changed our view of the world.” The second edition also acknowledged another great scientist, Nico van Kampen, whose beautiful lectures on stochastic processes, and critically humorous view of everything, were an inspiration and spurred my interest statistical physics. Although both of these great people are now gone, I thank them both.
The world exists and is stable because of a few symmetries at the microscopic level. Statistical physics explains how thermodynamics, and the incredible complexity of the world around us, emerges from those symmetries. This book attempts to tell the story of how that happens.
Austin, Texas January 2016
L. E. Reichl
1Introduction
Thermodynamics, which is a macroscopic theory of matter, emerges from the symmetries of nature at the microscopic level and provides a universal theory of matter at the macroscopic level. Quantities that cannot be destroyed at the microscopic level, due to symmetries and their resulting conservation laws, give rise to the state variables upon which the theory of thermodynamics is built.
Statistical physics provides the microscopic foundations of thermodynamics. At the microscopic level, many-body systems have a huge number of states available to them and are continually sampling large subsets of these states. The task of statistical physics is to determine the macroscopic (measurable) behavior of many-body systems, given some knowledge of properties of the underlying microscopic states, and to recover the thermodynamic behavior of such systems.
The field of statistical physics has expanded dramatically during the last half-century. New results in quantum fluids, nonlinear chemical physics, critical phenomena, transport theory, and biophysics have revolutionized the subject, and yet these results are rarely presented in a form that students who have little background in statistical physics can appreciate or understand. This book attempts to incorporate many of these subjects into a basic course on statistical physics. It includes, in a unified and integrated manner, the foundations of statistical physics and develops from them most of the tools needed to understand the concepts underlying modern research in the above fields.
There is a tendency in many books to focus on equilibrium statistical mechanics and derive thermodynamics as a consequence. As a result, students do not get the experience of traversing the vast world of thermodynamics and do not understand how to apply it to systems which are too complicated to be analyzed using the methods of statistical mechanics. We will begin in Chapter 2, by deriving the equations of state for some simple systems starting from our knowledge of the microscopic states of those systems (the microcanonical ensemble). This will give some intuition about the complexity of microscopic behavior underlying the very simple equations of state that emerge in those systems.
In Chapter 3, we provide a thorough grounding in thermodynamics. We review the foundations of thermodynamics and thermodynamic stability theory and devote a large part of the chapter to a variety of applications which do not involve phase transitions, such as heat engines, the cooling of gases, mixing, osmosis, chemical thermodynamics, and batteries. Chapter 4 is devoted to the thermodynamics of phase transitions and the use of thermodynamic stability theory in analyzing these phase transitions. We discuss first-order phase transitions in liquid–vapor–solid transitions, with particular emphasis on the liquid–vapor transition and its critical point and critical exponents. We also introduce the Ginzburg–Landau theory of continuous phase transitions and discuss a variety of transitions which involve broken symmetries. And we introduce the critical exponents which characterize the behavior of key thermodynamic quantities as a system approaches its critical point.
In Chapter 5, we derive the probability density operator for systems in thermal contact with the outside world but isolated chemically (the canonical ensemble). We use the canonical ensemble to derive the thermodynamic properties of a variety of model systems, including semiclassical gases, harmonic lattices and spin systems. We also introduce the concept of scaling of free energies as we approach the critical point and we derive values for critical exponents using Wilson renormalization theory for some particular spin lattices.
In Chapter 6, we derive the probability density operator for open systems (the grand canonical ensemble), and use it to discuss adsorption processes, properties of interacting classical gases, ideal quantum gases, Bose–Einstein condensation, Bogoliubov mean field theory, diamagnetism, and super-conductors.
The discrete nature of matter introduces fluctuations about the average (thermodynamic) behavior of systems. These fluctuations can be measured and give valuable information about decay processes and the hydrodynamic behavior of many-body systems. Therefore, in Chapter 7 we introduce the theory of Brownian motion which is the paradigm theory describing the effect of underlying fluctuations on macroscopic quantities. The relation between fluctuations and decay processes is the content of the so-called fluctuation–dissipation theorem which is derived in this chapter. We also derive Onsager’s relations between transport coefficients, and we introduce the mathematics needed to introduce the effect of causality on correlation functions. We conclude this chapter with a discussion of thermal noise and Landauer conductivity in ballistic electron waveguides.
Chapter 8 is devoted to hydrodynamic processes for systems near equilibrium. We derive the Navier–Stokes equations from the symmetry properties of a fluid of point particles, and we use the derived expression for entropy production to obtain the transport coefficients for the system. We also use the solutions of the linearized Navier–Stokes equations to predict the outcome of light-scattering experiments. We next derive a general expression for the entropy production in binary mixtures and use this theory to describe thermal and chemical transport processes in mixtures, and in electrical circuits. We conclude Chapter 8 with a derivation of hydrodynamic equations for superfluids and consider the types of sound that can exist in such fluids.
In Chapter 9, we derive microscopic expressions for the coefficients of diffusion, shear viscosity, and thermal conductivity, starting both from mean free path arguments and from the Boltzmann and Lorentz–Boltzmann equations. We obtain explicit microscopic expressions for the transport coefficients of a hard-sphere gas.
Finally, in Chapter 10 we conclude with the fascinating subject of nonequilibrium phase transitions. We show how nonlinearities in the rate equations for chemical reaction–diffusion systems lead to nonequilibrium phase transitions which give rise to chemical clocks, nonlinear chemical waves, and spatially periodic chemical structures, while nonlinearities in the Rayleigh–Bénard hydrodynamic system lead to spatially periodic convection cells.
The book contains Appendices with background material on a variety of topics. Appendix A, gives a review of basic concepts from probability theory and the theory of stochastic processes. Appendix B reviews the theory of exact differentials which is the mathematics underlying thermodynamics. In Appendix C, we review ergodic theory. Ergodicity is a fundamental ingredient for the microscopic foundations of thermodynamics. In Appendix D, we derive the second quantized formalism of quantum mechanics and show how it can be used in statistical mechanics. Appendix E reviews basic classical scattering theory. Finally, in Appendix F, we give some useful math formulas and data. Appendix F also contains solutions to some of the problems that appear at the end of each chapter.
The material covered in this textbook is designed to provide a solid grounding in the statistical physics underlying most modern physics research topics.
