ISBN-10:
0471328391
ISBN-13:
9780471328391
Pub. Date:
01/28/2000
Publisher:
Wiley, John & Sons, Incorporated
Equilibrium Statistical Mechanics / Edition 1

Equilibrium Statistical Mechanics / Edition 1

by Gene F. Mazenko

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Product Details

ISBN-13: 9780471328391
Publisher: Wiley, John & Sons, Incorporated
Publication date: 01/28/2000
Pages: 630
Product dimensions: 6.36(w) x 9.57(h) x 1.31(d)

About the Author

GENE F. MAZENKO, PhD, is a professor in the Department of Physics at the University of Chicago.

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PREFACE

It is the intention of this graduate-level text to present statistical mechanics from the modern condensed matter physics point of view. This approach emphasizes symmetry principles, conservation laws, and the consequences of broken symmetry. Pioneered by Landau and emphasized by Anderson, the notions of symmetry and broken symmetry are now understood as crucial to a fundamental understanding of statistical physics. The existence of a closed set of macrovariables, along with the second law of thermodynamics, forms the fundamental basis for statistical mechanics and thermodynamics. The general identification of the macrovariables for complex systems requires an understanding of conservation laws and the consequences of a broken continuous symmetry. The focus here is on the role of broken translational symmetry in treating solids. This involves an appreciation of the fundamental difference in the ability of solids to sustain certain applied mechanical forces compared to fluids.

Another motivation for writing this book is to highlight the approach of coarse graining in statistical mechanics. Coarse graining is a shorthand term for averaging over a set of microscopic degrees of freedom to obtain a self-consistent description of the same system at longer length scales. This approach becomes essential as physicists treat more complex systems on the mesoscopic and macroscopic spatial scales. Although there has been recent focus on coarse graining due to the brilliant success of the renormalization group approach to critical phenomena, this approach has a long, rich, and less specialized history. Indeed, hydrodynamics and elastic theory are classic examples of coarse graining and were developed as theories almost two hundred years ago. More recently, we have come to recognize thermodynamics as a coarse-grained version of statistical mechanics. In Chapter 4 the ideas of coarse graining are discussed in some generality, and then a number of examples are discussed.

The first three chapters, with some selection, make up a conventional one-quarter or one-semester course in statistical mechanics for a general collection of physics and chemistry students. There is more than enough material in Chapters 4 to 6 to fill out the rest of a year-long course. The level of discussion in Chapters 4 to 6 is in somewhat more depth than in the earlier chapters, but there is an effort to keep the mathematical presentation in the book at a level where experimental students are comfortable. More sophisticated material is treated in appendices.

Thermodynamics is treated at two levels. In Chapter 1 it is shown how thermodynamics follows smoothly from statistical mechanics in the case of fluids. Then, in Chapter 2, following the presentation in the classic text by Callen, the general formal structure of thermodynamics is presented. This approach will not appeal to all since it appears to be highly abstract and removed from any specific application. Such is the burden of a universal theory. In my own opinion, a less structured approach to thermodynamics has a tendency to circle around and hide the more general structure.

It is important, as emphasized in Chapters 4 through 6, that students understand the interplay between theory and experiment. This requires some discussion of historical development and I try to give some feeling for the enduring quality of a good, simple idea, such as the Debye approximation in treating solids. By giving some historical background on various topics, I hope to expose students to how science plays out over time. When starting a project there should be a constructive mixture of appreciation for what has been accomplished previously and the need for a fresh point of view.

In presenting statistical mechanics one always has a problem deciding what to do with ergodic theory. My own experience has been that physics students enjoy being introduced to this material when mixed in with some ideas from dynamical systems. On the other hand, if one treats this material in a one-quarter or one-semester course, one has to cut other important topics. Since the basics of statistical mechanics can be developed without a substantial reference to ergodic theory, I have chosen to put this material into an appendix. Several other more mathematical topics have also been put into appendices.

In Chapters 1 and 6 I have included material associated with the very different response properties of fluids and solids to applied mechanical forces. The emphasis is on the new aspects of the problem associated with broken translational symmetry and the need to change thermodynamics from the form describing the fluid phase to the description for solids, which requires including elastic degrees of freedom. In my experience this very general connection between broken continuous symmetry and need to modify thermodynamics is not widely appreciated.

The plan is to follow this introductory volume, with three additional volumes:

2. Fluctuations, Phase Transitions, and Defects
3. Nonequilibrium Statistical Mechanics
4. Field-Theoretic Methods in Equilibrium and Nonequilibrium Statistical Mechanics

Since some topics will be treated in detail in subsequent volumes, they are deemphasized in this beginning volume. For example, equilibrium spatial structure is not emphasized in Volume 1 since it will be treated in detail in Volume 2. Similarly, detailed discussions of nonequilibrium behavior and field theoretical ideas are delayed until later volumes. Certain very important material is not treated in this series. For example, the currently very active fields of random or quenched systems and strongly coupled electronic systems are mentioned only in passing.

I thank Professor Oriol Valls for detailed comments on an earlier version of this book. My wife, Judy, has given me, in her own special way, substantial support during this project. I dedicate this work to her.

Table of Contents

General Principles of Statistical Mechanics.

Principles of Thermodynamics.

Quantum Statistical Mechanics.

Statistical Mechanics of Fluids.

Equilibrium Properties of Dielectric and Magnetic Materials.

Statistical Mechanics in Solids.

Appendices.

Index.

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