Statistical Mechanics: Fundamentals and Model Solutions

Suitable for advanced undergraduates and graduate students, this volume presents a mathematical introduction to thermodynamics and statistical mechanics. Prerequisites include a familiarity with probability theory, real analysis, and the basics of Newtonian mechanics. The three-part approach covers thermodynamics, the fundamentals of statistical mechanics, and a detailed treatment of some model applications.

The text stresses the role of convexity in thermodynamics and provides simple results related to convex functions in the one-dimensional case. The approach to statistical mechanics is based on quantum mechanics and large-deviation theory, which receive a detailed examination. The final part's analysis of model systems includes the Ising model, the mean-field lattice gas, the free electron gas, Chandrasekhar's theory of white dwarf stars, bosons with interaction, and a simple model for superconductivity. Each section concludes with a set of problems, for which complete solutions appear at the end. Helpful appendixes on mathematical probability theory, quantum mechanics, and superconductivity conclude the text.