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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 are 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.