Elementary Lectures in Statistical Mechanics

I Fundamentals: Separable Classical Systems.- Lecture 1. Introduction.- 1.1 Historical Perspective.- 1.2 Basic Principles.- 1.3 Author's Self-Defense.- 1.4 Other Readings.- References.- Lecture 2. Averaging and Statistics.- 2.1 Examples of Averages.- 2.2 Formal Averages.- 2.3 Probability and Statistical Weights.- 2.4 Meaning and Characterization of Statistical Weights.- 2.5 Ideal Time and Ensemble Averages.- 2.6 Summary.- Problems.- References.- Lecture 3. Ensembles: Fundamental Principles of Statistical Mechanics.- 3.1 Ensembles.- 3.2 The Canonical Ensemble.- 3.3 Other Ensembles.- 3.4 Notation and Terminology: Phase Space.- 3.5 Summary.- Problems.- References.- Lecture 4. The One-Atom Ideal Gas.- 4.1 The Classical One-Atom Ensemble.- 4.2 The Average Energy.- 4.3 Mean-Square Energy.- 4.4 The Maxwell-Boltzmann Distribution.- 4.5 Reduced Distribution Functions.- 4.6 Density of States.- 4.7 Canonical and Representative Ensembles.- 4.8 Summary.- Problems.- References.- Aside A. The Two-Atom Ideal Gas.- A.1 Setting Up the Problem.- A.2 Average Energy.- A.3 Summary.- Problems.- Lecture 5. N-Atom Ideal Gas.- 5.1 Ensemble Average for N-Atom Systems.- 5.2 Ensemble Averages of E and E2.- 5.3 Fluctuations and Measurements in Large Systems.- 5.4 Potential Energy Fluctuations.- 5.5 Counting States.- 5.6 Summary.- Problems.- References.- Lecture 6. Pressure of an Ideal Gas.- 6.1 P from a Canonical Ensemble Average.- 6.2 P from the Partition Function.- 6.3 P from the Kinetic Theory of Gases.- 6.4 Remarks.- Problems.- References.- Aside B. How Do Thermometers Work-The Polythermal Ensemble.- B.1 Introduction.- B.2 The Polythermal Ensemble.- B.3 Discussion.- Problems.- References.- Lecture 7. Formal Manipulations of the Partition Function.- 7.1 The Equipartition Theorem.- 7.2 First Generalized Equipartition Theorem.- 7.3 Second Generalized Equipartition Theorem.- 7.4 Additional Tests; Clarification of the Equipartition Theorems.- 7.5 Parametric Derivatives of the Ensemble Average.- 7.6 Summary.- Problems.- References.- Aside C. Gibbs's Derivation of.- References.- Lecture 8. Entropy.- 8.1 The Gibbs Form for the Entropy.- 8.2 Special Cases.- 8.3 Discussion.- Problems.- References.- Lecture 9. Open Systems; Grand Canonical Ensemble.- 9.1 The Grand Canonical Ensemble.- 9.2 Fluctuations in the Grand Canonical Ensemble.- 9.3 Discussion.- Problems.- References.- II Separable Quantum Systems.- Lecture 10. The Diatomic Gas and Other Separable Quantum Systems.- 10.1 Partition Functions for Separable Systems.- 10.2 Classical Diatomic Molecules.- 10.3 Quantization of Rotational and Vibrational Modes.- 10.4 Spin Systems.- 10.5 Summary.- Problems.- References.- Lecture 11. Crystalline Solids.- 11.1 Classical Model of a Solid.- 11.2 Einstein Model.- 11.3 Debye Model.- 11.4 Summary.- Problems.- References.- Aside D. Quantum Mechanics.- D.1 Basic Principles of Quantum Mechanics.- D.2 Summary.- Problems.- References.- Lecture 12. Formal Quantum Statistical Mechanics.- 12.1 Choice of Basis Vectors.- 12.2 Replacement of Sums over All States with Sums over Eigenstates.- 12.3 Quantum Effects on Classical Integrals.- 12.4 Summary.- Problems.- References.- Lecture 13. Quantum Statistics.- 13.1 Introduction.- 13.2 Particles Whose Number Is Conserved.- 13.3 Noninteracting Fermi-Dirac Particles.- 13.4 Photons.- 13.5 Historical Aside: What Did Planck Do-.- 13.6 Low-Density Limit.- Problems.- References.- Aside E. Kirkwood-Wigner Theorem.- E.1 Momentum Eigenstate Expansion.- E.2 Discussion.- Problems.- References.- Lecture 14. Chemical Equilibria.- 14.1 Conditions for Chemical Equilibrium.- 14.2 Equilibrium Constants of Dilute Species from Partition Functions.- 14.3 Discussion.- Problems.- References.- III Interacting Particles and Cluster Expansions.- Lecture 15. Interacting Particles.- 15.1 Potential Energies; Simple Fluids.- 15.2 Simple Reductions; Convergence.- 15.3 Discussion.- Problems.- References.- Lecture 16. Cluster Expansions.- 16.1 Search for an Approach.-