UNIST · Fall 2026
Statistical Mechanics
A rigorous course in equilibrium statistical mechanics, from the foundations of ensemble theory to quantum gases, interacting systems, phase transitions, fluctuations, and response.
Objective
The course develops both the physical principles and the mathematical methods of statistical mechanics. Students are expected to understand the logic of the subject, reproduce central derivations, and use the formalism independently.
Topics
- Foundations: thermodynamic laws; microscopic and macroscopic states; entropy and probability; phase space; ensembles; ergodicity; Liouville’s theorem; the thermodynamic limit; the Gibbs paradox; the virial theorem.
- Ensembles: microcanonical, canonical, and grand-canonical ensembles; partition functions; thermodynamic potentials; energy and particle-number fluctuations; equipartition; harmonic oscillators; paramagnetism; phase equilibrium.
- Ideal gases: classical gases; density matrices; indistinguishable particles; Bose–Einstein and Fermi–Dirac statistics; black-body radiation; Bose–Einstein condensation; degenerate Fermi gases; internal degrees of freedom; magnetic response.
- Interacting systems: virial and cluster expansions; correlations; the second virial coefficient; the van der Waals fluid; stability and liquid–gas coexistence.
- Phase transitions: first-order and continuous transitions; magnetic and lattice-gas models; spontaneous symmetry breaking; Landau and mean-field theories; transfer matrices; correlation length; critical exponents; critical dimensions; scaling and universality.
- Fluctuations and response: thermodynamic fluctuations; spatial and temporal correlations; linear response; fluctuation–dissipation theorem; Onsager relations; relaxation and ergodicity breaking.
Books
Principal text: R. K. Pathria and Paul D. Beale, Statistical Mechanics.
Supplementary reference: L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1.
Lecture notes
Handwritten notes may contain errors. Corrections will be discussed in class.
- Statistical basis of thermodynamics
- Ensemble theory
- Canonical ensemble
- Grand-canonical ensemble
- Quantum statistics
- Theory of simple gases
- Ideal Bose systems
Assessment
| Quizzes | 30% |
| Midterm examination | 30% |
| Final examination | 40% |
Quizzes may be announced or unannounced and will test conceptual understanding, derivations, and problem-solving ability. Practice problems may be assigned but will not necessarily be graded.
Requirements
Attendance and active participation are required. AI tools may be used for private study outside class, but are prohibited during quizzes and examinations. Students remain responsible for every derivation, argument, and result they submit or present.