Statistical Mechanics

From microstates to the renormalization group.

Syllabus

  1. Foundations

    1. Microstates, Macrostates & Phase Space
    2. Boltzmann Entropy & the Microcanonical Ensemble
    3. Temperature, Pressure & Chemical Potential

  2. Canonical & Grand Canonical Ensembles

    1. The Boltzmann Distribution & the Partition Function
    2. Free Energy & Thermodynamics from Z
    3. Equipartition, the Ideal Gas & Fluctuations
    4. The Grand Canonical Ensemble & Chemical Potential

  3. Quantum Statistics

    1. Indistinguishability — MB, BE & FD Statistics
    2. The Degenerate Fermi Gas
    3. Bose–Einstein Condensation
    4. Photons & Phonons — The Quantum Gases of Light and Sound

  4. Interacting Systems & Phase Transitions

    1. Van der Waals & the Liquid–Gas Transition
    2. The Ising Model & Mean-Field Theory
    3. Critical Phenomena — Scaling & Universality
    4. The Renormalization Group

  5. Non-Equilibrium & Computational

    1. Kinetic Theory & Transport
    2. The Fluctuation–Dissipation Theorem
    3. Monte Carlo Methods