Intro to Statistical Mechanics; Statistical Mechanics in a Nutshell

August 2012 When students are first exposed at the undergraduate or graduate level to statistical mechanics, they are still processing the tools and concepts of classical mechanics, quantum mechanics, and electromagnetism. Thus it is important that a statistical mechanics course…

August 2012

When students are first exposed at the undergraduate or graduate level to statistical mechanics, they are still processing the tools and concepts of classical mechanics, quantum mechanics, and electromagnetism. Thus it is important that a statistical mechanics course include expert teaching and guidance to relate that course’s concepts to students’ emerging interests. And students who eventually become researchers will find it helpful to have understandable textbooks with which they can quickly reference important details for successful application of statistical mechanics.

Two new statistical mechanics texts provide clarity on the subject’s key concepts and applications. Introduction to Statistical Mechanics by John Dirk Walecka makes the subject inviting and reads as a nice sequel to his Fundamentals of Statistical Mechanics: Manuscript and Notes of Felix Bloch (Stanford University Press, 1989; reviewed by Robert Pelcovits in Physics Today, July 1990, page 69), which Walecka prepared and edited. Statistical Mechanics in a Nutshell by Luca Peliti is a more sophisticated presentation that will be of value to advanced students, lecturers, and practitioners.

Walecka’s edited Bloch notes influenced my views on phase space, classical versus quantum pictures, and the density-matrix formalism. I recall Walecka writing in the preface that he intended to use Bloch’s approach to teaching the subject, so I engaged Walecka’s Introduction to Statistical Mechanics with an expectation of déjà vu. However, I found the newer work to be an original and appealing presentation and not a recast of Bloch’s notes.

Overall, the text’s practical feel will give students a good sense of what it means to use statistical mechanics; that achievement is also shared by Ryōgo Kubo’s Statistical Mechanics: An Advanced Course with Problems and Solutions (2nd edition, North-Holland, 1988). Walecka provides a clear narrative with several standard calculations that students are often left alone to figure out on their own. One example concerns the method of steepest descent, an important technique used in several areas of physics. He also presents various applications of statistical ensembles, particularly in the section on molecular spectroscopy. In the classroom, applications tend to be limited to the problem sets, yet in this case students will gain from Walecka’s descriptive treatment of diatomic or polyatomic molecules in explaining molecular spectroscopy. Moreover, he also plants seeds for future learning in the chapter “Special topics,” which includes discussions of mean-field theory and order–disorder transitions.
Promising though it is as introductory text, Introduction to Statistical Mechanics contains some awkward notation. Instead of using the widely accepted β, Walecka writes out 1/kBT. Also, I found it initially off-putting to see the partition function labeled as “p.f.,” though I came to appreciate that label more when I thought about how much effort it takes to write symbols for partition functions of different canonical ensembles. Such stylistic choices in notation and labeling may bog down students, who should be focused on applying the tools of statistical mechanics to real, physical systems. I believe Walecka’s notations were intended to dissuade students from rote memorization and to focus them on a physical understanding of temperature and on building the correct partition function.
Peliti’s Statistical Mechanics in a Nutshell—originally published in Italian (Bollati Boringhieri, 2003)—is a fantastic reference for those who know the subject, teach it, or need a quick technical reminder, especially on the topic of phase transitions, which are consistently featured in modern-day discussions and one that Walecka’s book omits. Browsing Peliti’s book reminded me of such texts as Kerson Huang’s Statistical Mechanics (2nd edition, Wiley, 1987); David Chandler’s Introduction to Modern Statistical Mechanics (Oxford University Press, 1987); and Mehran Kardar’s Statistical Physics of Particles and Statistical Physics of Fields (both published by Cambridge University Press, 2007).

Of the books under review, Statistical Mechanics in a Nutshell provides the more general overview, with topics such as the renormalization group method. It includes a good mix of fundamental thermodynamics, phase behavior, and other key subjects. Even so, I do not see it as a standalone book for introductory students, even if they are energetic and serious; they will need an expert teacher or practitioner to make the ideas become more vivid in the classroom.

Physics Today