PH4211: Statistical Mechanics
“ Ludwig Boltzmann, who spent much of his life studying Statistical Mechanics, died in 1906,
by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our
turn to study Statistical Mechanics.
Perhaps it will be wise to approach the subject cautiously.”
in States of Matter, by David. L. Goodstein, 1975, Dover N.Y.
This is an advanced level course on Statistical and Thermal Physics; it builds on the
material learned by students in their first three years. The course starts with
a review of the formal structure of Statistical Mechanics and Thermodynamics considered
from a unified viewpoint. There is a brief revision of non-interacting systems. Following this the emphasis is on interacting
systems. First weakly interacting systems are considered, where the interest is in
seeing how such interactions cause small deviations from the non-interacting case. Following
this, systems are examined where interactions lead to drastic changes: namely phase
transitions. A number of specific examples is considered and these are unified within the
Landau theory of phase transitions. The final section of the course considers
non-equilibrium systems and the way these evolve towards equilibrium. Here fluctuations
play a vital role, as is formalised in the Fluctuation-Dissipation theorem.
Revision Class 2020
Course Notes The the material is now available in book form - see Book List above. But a very drafty draft version of Edition 2 is available here.
- Contents Note: the course comprises only a selection
of the topics covered in these notes.
- Chapter 1 The Methodology of Statistical Mechanics
- Chapter 2 Practical Calculations with Ideal Systems
- Chapter 3 Non-ideal Gases
- Chapter 4 Phase Transitions
- Chapter 5 Fluctuations and Dynamics
- Founders of thermodynamics and suicide.
- E. Cornell: Very Cold Indeed: The Nanokelvin Physics of Bose-Einstein Condensation - J. Res. Natl. Inst. Stand. Technol. 101, 419 (1996)
- W. Mullin: A New Derivation of the Virial Expansion - Am. J. Phys. 40, 1473 (1972)
- S. Brush: History of the Lenz-Ising Model - Rev. Mod. Phys. 39, 883 (1967)
- D. Bitko: Quantum Critical Behaviour for a Model Magnet - Phys. Rev. Lett. 77, 940 (1996)
- J. Als-Nielsen and R. J. Birgeneau: Mean field theory, the Ginzburg criterion, and marginal dimensionality of phase transitions - Am. J. Phys. 45, 554 (1977)
- Brian J. Ford: Brownian Movement in Clarkia Pollen: A Reprise of the First Observations - The Microscope, 40 (4), 235 (1992)
- S. Braun et al.: Negative Absolute Temperatures for Motional Degrees of Freedom - Science 339, 52 (2013)
- A. J. Leggett: On the minimum entropy of a large system at low temperatures - Ann. Phys. 72, 80 (1972)
Problem Assignments and Solutions
Past Examination Papers
This page is still under construction; indeed it will continue so until the course is no longer taught.
Brian Cowan - E-mail: