Notes for Statistical Mechanics I

This contains PDF files for the class notes. They are posted after we complete a one- to-two week section of material:

  • Part 1  – Classical Mechanics, Lagrangian & Hamiltonian formulations, Exact Differentials, Canonical Transformations, Action/Angle Variables
  • Part 2 – A simple quantum picture of Entropy, review of Probability & Statistics, The Boltzmann Expression for Entropy, Extensivity and Maximizing the Entropy with constraints, The Ergodic Hypothesis, Liouville’s theorem, Ensembles
  • Part 3 – Extensivity and constraints predict Boltzmann weights, The Partition Function, Tricks with the Partition Function, Derivation of the Ideal Gas law, translational, electronic, vibrational, and rotational partition functions, Equipartition,
  • Part 4 – Thermodynamics: State Variables, Laws, Heat, Work, Reversibility, Stirling’s Approximation, Chemical Equilibria, the Grand Canonical Ensemble, Quantum statistics, Fermi levels, Bose-Einstein condensates, Models for Crystals (Einstein, and Debye)
  • Part 5 – Phase transitions, The Ising Model, Frustration, Critical Exponents, Transfer Matrices, Exact solution of Ising in 1-D.
  • Part 6 – Peierls’ Theorem, Mean Field Theory
  • Part 7 – Liquids, Reduced Distribution Functions, g(r), reversible work theorem,
  • Part 8 – Monte Carlo methods, Molecular Dynamics, time correlation functions, Green-Kubo relations, Transition State Theory