Syllabus

Main Texts:

Introduction to Modern Statistical Mechanics, by David Chandler
Statistical Mechanics, by Donald A. McQuarrie

Other useful texts:

See the Book List for a list of texts on reserve. We will be referring most frequently to Hansen & McDonald or Huang when the primary texts don't contain a topic of interest.

Weeks 1-2: Mathematical Review, Classical Mechanics, Ensembles (McQuarrie, Chapters 1-3 and Chandler, Chapter 3)

1. Lagrangian Formulation
2. Hamiltonian Formulation
3. Poisson Brackets and Canonical Transformations
4. Ensembles and Phase Space
5. Liouville's Theorem
6. Equilibrium Statistical Mechanics and it's ensembles

Week 3: Elementary Probability Theory

1. Distributions and Averages
2. Cumulants and Fluctuations
3. The Central Limit Theorem

Week 4: Distributions & Fluctuations (Chandler, Chapter 3)

1. Theory of Ensembles, Classical and Quantum
2. Equivalence of Ensembles
3. Fluctuations of Macroscopic Observables

Week 5: Basic Thermodynamics (Chandler, Chapter 1)

1. Review of Concepts
2. The Laws of Thermodynamics
3. Legendre Transforms
4. The Maxwell Relations
5. The Gibbs-Duhem Equation and Extensive Functions
6. Intensive Functions

Weeks 6-7: Phases & Transitions, The Ising Model (Chandler, Chapter 5)

1. Stability of Thermodynamics Phases
2. First-order Phase transitions
3. Interfaces
4. The Ising Model
5. Lattice Gas
6. Broken Symmetry
7. Mean Field Theory

Weeks 8-9: Methodology (Chandler, Chapter 6)

1. Monte Carlo
2. Trajectories
3. Non-Boltzmann Sampling

Weeks 10-11: A brief introduction to Liquid Theory (Chandler, Chapter 7 and McQuarrie, Chapter 13)

1. Averages
2. Distribution Functions
3. Reversible Work Theorem
4. g(r)
5. Molecular liquids

Weeks 12-13: Non-equilibrium systems (Chandler, Chapter 8 and McQuarrie Chapters 19-21)

1. Fluctuation-Dissipation Theorem
2. Onsager's Regression Hypothesis
3. Brownian Motion, Friction and the Langevin Equation
4. Transport
5. Time Correlation Functions