Elementary Lectures in Statistical Mechanics, 2000 Graduate Texts in Contemporary Physics Series

This volume is based on courses on Statistical Mechanics which I have taught for many years at the Worcester Polytechnic Institute. My objective is to treat classical statistical mechanics and its modem applications, especially interacting particles, correlation functions, and time-dependent phenomena. My development is based primarily on Gibbs's ensemble formulation. Elementary Lectures in Statistical Mechanics is meant as a (relatively sophis­ ticated) undergraduate or (relatively straightforward) graduate text for physics students. It should also be suitable as a graduate text for physical chemistry stu­ dents. Physicists may find my treatment of algebraic manipulation to be more explicit than some other volumes. In my experience some of our colleagues are perhaps a bit over-enthusiastic about the ability or tendency of our students to complete gaps in the derivations. I emphasize a cyclic development of major themes. I could have begun with a fully detailed formal treatment of ensemble mechanics, as found in Gibbs's volume, and then given material realizations. I instead interleave formal discussions with simple concrete models. The models illustrate the formal definitions. The approach here gives students a chance to identify fundamental principles and methods before getting buried in ancillary details.

I Fundamentals: Separable Classical Systems.- Lecture 1. Introduction.- Lecture 2. Averaging and Statistics.- Lecture 3. Ensembles: Fundamental Principles of Statistical Mechanics.- Lecture 4. The One-Atom Ideal Gas.- Aside A. The Two-Atom Ideal Gas.- Lecture 5. N-Atom Ideal Gas.- Lecture 6. Pressure of an Ideal Gas.- Aside B. How Do Thermometers Work—The Polythermal Ensemble.- Lecture 7. Formal Manipulations of the Partition Function.- Aside C. Gibbs’s Derivation of.- Lecture 8. Entropy.- Lecture 9. Open Systems; Grand Canonical Ensemble.- II Separable Quantum Systems.- Lecture 10. The Diatomic Gas and Other Separable Quantum Systems.- Lecture 11. Crystalline Solids.- Aside D. Quantum Mechanics.- Lecture 12. Formal Quantum Statistical Mechanics.- Lecture 13. Quantum Statistics.- Aside E. Kirkwood-Wigner Theorem.- Lecture 14. Chemical Equilibria.- III Interacting Particles and Cluster Expansions.- Lecture 15. Interacting Particles.- Lecture 16. Cluster Expansions.- Lecture 17. ? via the Grand Canonical Ensemble.- Lecture 18. Evaluating Cluster Integrals.- Lecture 19. Distribution Functions.- Lecture 20. More Distribution Functions.- Lecture 21. Electrolyte Solutions, Plasmas, and Screening.- IV Correlation Functions and Dynamics.- Lecture 22. Correlation Functions.- Lecture 23. Stability of the Canonical Ensemble.- Aside F. The Central Limit Theorem.- Lecture 24. The Langevin Equation.- Lecture 25. The Langevin Model and Diffusion.- Lecture 26. Projection Operators and the Mori-Zwanzig Formalism.- Lecture 27. Linear Response Theory.- V A Research Problem.- Aside G. Scattering of Light, Neutrons, X-Rays, and Other Radiation.- Lecture 28. Diffusion of Interacting Particles.- Lecture 29. Interacting Particle Effects.- Lecture 30. Hidden Correlations.