1. Brief review of thermal physics
Extensive and intensive variables, laws of thermodynamics, entropy and Gibbs paradox, Legendre transformation, thermodynamic potentials, chemical potential, Jacobian determinant, Maxwell’s relations and their applications.
2. Statistical description of many-particle systems
Binomial, Gaussian, and Poisson distributions, central limit theorem. Phase space, Liouville’s theorem. Microstates and macrostates, statistical ensemble, statistical postulates, probability calculations, accessible states, constraint, equilibrium, irreversibility.
3. Equilibrium statistical mechanics
Microcanonical ensemble. Canonical ensemble: Boltzmann factor, Boltzmann distribution, canonical partition function and thermodynamic quantities, energy fluctuations, applications of canonical ensemble. Grand canonical ensemble: Gibbs factor, Gibbs distribution, grand partition function and thermodynamic quantities, particle number fluctuations, applications of grand canonical ensemble. Equipartition theorem: proof of the theorem, applications, specific heat of solids. Maxwell–Boltzmann statistics.
4. Quantum statistics
Bosons: occupation number, Bose-Einstein statistics, specific heat of solids (Einstein model and Debye theory), black-body radiation, Bose-Einstein condensation. Fermions: occupation number, Fermi-Dirac statistics, degenerate Fermi gas.
5. Phase equilibria and phase transitions
Equilibrium condition, phase diagrams of some simple systems, Clausius-Clapeyron equation, critical point, first order and second order phase transitions, Ising model.
Frederick Reif, Fundamentals of Statistical and Thermal Physics.
Mehran Kardar, Statistical Physics of Particles.
Daniel V. Schroeder, An introduction to thermal physics.
R. K. Pathria and Paul D. Beale, Statistical Mechanics (Third Edition).
L. D. Landau and E. M. Lifshitz, Statistical Physics, Third Edition, Part 1: Volume 5.
Kerson Huang, Statistical Mechanics (Second Edition).
Harvey Gould and Jan Tobochnik, Statistical and Thermal Physics: With Computer Applications.
James P. Sethna, Statistical Mechanics: Entropy, Order Parameters and Complexity.
Examinations