# PH 613,4: Statistical Mechanics

## W,S 2013 (D. Belitz)

### Chapter 1: Principles of Statistical Mechanics

\$1: Hamilton's equations
1.1 Hamilton's equations, and phase space
1.2 Phase flow
1.3 Liouville's theorem
1.4 Poicare's theorem
1.5 Necessity of a statistical description of many-particle systems

\$2: Elements of probability theory
2.1 The definition of probability
2.2 Discrete random variables
2.3 Continuous random variables
2.4 Averages and fluctuations
2.5 The binomial distribution
2.6 The Gaussian or normal distribution
2.7 The central limit theorem

\$3: Review of thermodynamics
3.1 Statistical description of large systems
3.2 The equilibrium state
3.3 Interacting systems
3.4 Reversible and irreversible processes
3.5 Energy, temperature, and entropy
3.6 The laws of thermodynamics
3.7 Thermodynamic potentials

\$4: Statistical ensembles
4.1 Gibbsian ensembles
4.2 The microcanonical ensemble
4.3 The canonical ensemble
4.4 The grand canonical ensemble
4.5 The thermodynamic limit, and the Duhem-Gibbs relation
4.6 Systems in magnetic fields

\$5: Quantum statistical mechanics
5.1 The postulates of quantum statistical mechanics
5.2 The statistical operator for various ensembles
5.3 Fermions and bosons
5.4 The Fermi-Dirac distribution
5.5 The Bose-Einstein distribution

### Chapter 2: Selected Applications

\$1: Classical systems
1.1 The classical, monatomic ideal gas
1.3 The equipartition theorem
1.4 Maxwell's velocity distribution I: Canonical ensemble
1.5 Maxwell's velocity distribution II: Microcanonical ensemble

\$2: The ideal Fermi gas
2.1 Distribution functions, and the equation of state (for both fermions and bosons)
2.2 The degenerate electron gas
2.3 The specific heat of the degenerate electron gas (Sommerfeld expansion)
2.4 Pauli paramagnetism
2.5 Landau diamagnetism

\$3: The ideal Bose gas
3.1 Bose-Einstein condensation
3.2 Chemical potential and particle number for T < T0
3.3 The specific heat of an ideal Bose gas