Topics in Statistical Mechanics

Building on the material learned by students in their first few years of study, this book presents an advanced level course on statistical and thermal physics. It begins with a review of the formal structure of statistical mechanics and thermodynamics considered from a unified viewpoint. After a brief revision of non-interacting systems, emphasis is laid 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. Second, systems are examined where interactions lead to drastic changes, namely phase transitions. A number of specific examples are given, and these are unified within the Landau theory of phase transitions. The final chapter of the book looks at non-equilibrium systems and the way these evolve towards equilibrium. Here, fluctuations play a vital role, as is formalized in the Fluctuation-Dissipation theorem.