Synopses & Reviews
"Excellent … a welcome addition to the literature on the subject." — Science
Before the publication of this standard, oft-cited book, there were few if any statistical-mechanics texts that incorporated reviews of both fundamental principles and recent developments in the field.
In this volume, Professor Hill offers just such a dual presentation — a useful account of basic theory and of its applications, made accessible in a comprehensive format. The book opens with concise, unusually clear introductory chapters on classical statistical mechanics, quantum statistical mechanics and the relation of statistical mechanics to thermodynamics. Then follows a wide-ranging, detailed examination of various applications. Chapter 4 deals with fluctuations. The fifth chapter treats the theory of imperfect gases and condensation, largely following Mayer's theory but also giving some new, alternative derivations and discussing in the final section Yang and Lee's theory. The sixth chapter is devoted to a discussion of distribution functions and the theory of the liquid state. Chapter 7 deals with nearest-neighbor (Ising) lattice statistics, while the last chapter discusses free-volume and hole theories of liquids and solids.
Written primarily for graduate students and researchers in chemistry, physics and biology who already have some acquaintance with statistical mechanics, the book lends itself to use as a text for a second course in statistical mechanics, as a supplement to a first course or for self-study or reference. The level is neither introductory nor highly sophisticated; the author has generally emphasized material that is not available in other books. In addition, selected bibliographic references at the end of each chapter suggest supplementary reading.
Synopsis
Standard text opens with clear, concise chapters on classical statistical mechanics, quantum statistical mechanics, and the relation of statistical mechanics to thermodynamics. Further topics cover fluctuations, the theory of imperfect gases and condensation, distribution functions and the liquid state, nearest neighbor (Ising) lattice statistics, and more.
Synopsis
Standard text covers classical statistical mechanics, quantum statistical mechanics, relation of statistical mechanics to thermodynamics, plus fluctuations, theory of imperfect gases and condensation, distribution functions and the liquid state, more.
Table of Contents
FOREWORD by John. G. Kirkwood
PREFACE
CHAPTER 1. PRINCIPLES OF CLASSICAL STATISTICAL MECHANICS
1. Statistical Mechanics and Thermodynamics
2. Phase Space
3. Ensembles
4. Postulate on the Use of Ensemble Averages
5. Postulate on the Form of the Distribution Function
6. Grand Ensembles
7. Ergodic Theory
CHAPTER 2. PRINCIPLES OF QUANTUM STATISTICAL MECHANICS
8. Review of Quantum Mechanics
9. Ensembles and Ensemble Averages in Quantum Statistical Mechanics
10. Postulate on the Use of Ensemble Averages
11. Postulate on the Form of the Density Matrix
12. Grand Ensembles
13. Derivation of Generalized Ensembles from the Microcanonical Ensemble
CHAPTER 3. STATISTICAL MECHANICS AND THERMODYNAMICS
14. Association of Thermodynamic Variables with Statistical Mechanical Quantities
15. Summary of Ensembles
16. Transition from Quantum to Classical Statistics
17. Entropy and Irreversibility in Thermodynamics
CHAPTER 4. FLUCTUATIONS
18. Introduction
19. Fluctuations According to the Various Ensembles
20. Thermodynamic Equivalence of Ensembles
21. Composition Fluctuations in Multicomponent Systems
CHAPTER 5. THEORY OF IMPERFECT GASES AND CONDENSATION
22. The Partition Function and Cluster Integrals
23. Pressure of the Gas Expressed as a Power Series in the Activity
24. Irreducible Cluster Integrals
25. The Virial Expansion for the Gas
26. Alternative Derivations
27. Exact Treatment of Physical Clusters
28. Theory of Condensation
CHAPTER 6. DISTRIBUTION FUNCTIONS AND THE THEORY OF THE LIQUID STATE
A. CANONICAL ENSEMBLE
29. Definition of Distribution and Correlation Functions
30. Thermodynamic Functions of a Fluid and the Radial Distribution Function
31. Potential of Mean Force and the Superposition Approximation
32. The Kirkwood Integral Equation
33. The Born-Green-Yvon Integral Equation
34. Radial Distribution Function and Superposition Approximation in Gases
35. Fluid of Hard Spheres According to the Superposition Approximation
36. Fluid with Modified Lennard-Jones Molecular Interaction Potential According to the Superposition Approximation
B. GRAND CANONICAL ENSEMBLE
37. "Distribution Functions in Monatomic, One-component Systems"
38. The Kirkwood-Salsburg Integral Equation
39. Distribution Functions at a Phase Transition
40. "Distribution Functions in Polyatomic, Multicomponent Systems"
CHAPTER 7. NEAREST-NEIGHBOR LATTICE STATISTICS
41. Thermodynamics and Interconnections
42. Exat and Formal Methods
43. One-dimensional Lattice
44. Two-dimensional Lattice
45. Three-dimensional Lattice
46. Approximate Methods
CHAPTER 8. LATTICE THEORIES OF THE LIQUID AND SOLID STATES
47. Communal Entropy and Free Volume
48. General Free-volume Theory
49. The Lennard-Jones and Devonshire Theory
50. Hole Theories of the Liquid and Solid States
APPENDIXES
1. Natural Constants
2. "One-component, Perfect Monatomic Gas"
3. Binary Perfect-gas Mixture
4. One-component Perfect Lattice Gas
5. Multilayer Gas Adsorption
6. Quantum and Classical Limits
7. Normalization of Radial Distribution Function
8. Glossary of Certain Definitions in Chapter 7
9. First-order Phase Transitions
10. Gas Adsorption on a Solid Surface
INDEX