Last Modified: February 11, 2002

This syllabus is tentative; however, I anticipate only minor variations.

Introduction to Classical Statistical Mechanics

(Definitions and some Philosophy)

• Subject of Statistical Mechanics
• Microscopic and Macroscopic States
• Ensembles. Averaging and Ergodicity
• Distribution function
• Role of Energy
• Entropy

Theory of Ensembles

• Microcanonical, Canonical, and Grand Canonical Ensembles
• Legendre Transformations and Equivalency of Ensembles
• Examples

Review of Thermodynamics

• Thermodynamic potentials
• Maxwell relations
• Variational methods
• Maximal Work, Minimal Work and Thermodynamic Stability

Gases, Solids, (Liquids)

Quantum Mechanical Foundations of Statistical Physics

Gases

• Ideal gas and other "ideal" models
• Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein statistics
• Theory of classical imperfect gases.
• Cluster (virial) expansion.
• van der Waals model.
• BEC
  

Solids

• Equipartition Theorem.
• Harmonic Oscillator.
• Einstein and Debye models of Solids.

Liquids (time permitting)

• Problems of liquids theory.
• Distribution and correlation functions.
• Perturbation theory.

Phase Equilibrium and Phase Transitions

• Chemical equilibria and solutions
• van der Waals equation of state
• Mean field theory
• Beyond mean field theory
• Landau theory

Fluctuations

• Fluctuations in Inhomogeneous Systems
• Time Dependent Fluctuations
• Time Correlation Functions
• Random Force
• Brownian Motion and Focker-Planck Equation