My intention in this textbook is to provide a self-contained exposition of the fundamentals and applications of statistical thermodynamics for beginning graduate students in the engineering sciences. Especially within engineering, most students enter a course in statistical thermodynamics with limited exposure to statistics, quantum mechanics, and spectroscopy. Hence, I have found it necessary over the years to “start from the beginning,” not leaving out intermediary steps and presuming little knowledge in the discrete, as compared to the continuum, domain of physics. Once these things are done carefully, I find that good graduate students can follow the ideas, and that they leave the course excited and satisfied with their newfound understanding of both statistical and classical thermodynamics.

Nevertheless, a first course in statistical thermodynamics remains challenging and sometimes threatening to many graduate students. Typically, all their previous experience is with the equations of continuum mechanics, whether applied to thermodynamics, fluid mechanics, or heat transfer. For most students, therefore, the mathematics of probability theory, the novelty of quantum mechanics, the confrontation with entropy, and indeed the whole new way of thinking that surrounds statistical thermodynamics are all built-in hills that must be climbed to develop competence and confidence in the subject. For this reason, although I introduce the ensemble method at the beginning of the book, I have found it preferable to build on the related Maxwell–Boltzmann method so that novices are not confronted immediately with the conceptual difficulties of ensemble theory.