Statistical Mechanics

Probability and large numbers
Large Numbers and FluctuationsCounting States W
The microcanonical ensemble
Equal a Priori ProbabilityBoltzmann's Relation S = k log WDefining TemperatureThe Gibbs ParadoxNegative TemperatureMaxwell's Demon and Landauer's Principle
The canonical ensemble
The Boltzmann FactorThe Partition Function ZEnergy Fluctuations and Heat CapacityThe Gibbs Entropy S = −k Σ p log pThe Minimum Free Energy PrincipleThe Maximum Entropy Principle
Applications
The Maxwell Distribution and the Ideal Gas LawEquipartition of EnergyThe Two-Level SystemThe Harmonic OscillatorThe Debye Model
Phase transitions
The Ising Model and Mean Field TheoryLandau TheoryThe van der Waals EquationThe One-Dimensional Ising Model and the Transfer Matrix
Quantum statistics
The Grand Canonical EnsembleFermi and Bose DistributionsThe Fermi GasBlack-Body RadiationBose-Einstein CondensationChemical EquilibriumThe Third Law of Thermodynamics
Time and fluctuations
Random Walks and DiffusionBrownian Motion and the Langevin EquationMonte Carlo and the Metropolis AcceptanceThe H Theorem and Irreversibility