Statistical Mechanics: Entropy, Order Parameters, and Complexity

Statistical Mechanics: Entropy, Order Parameters, and Complexity , James P. Sethna , Oxford U. Press, New York, 2006. $99.50, $44.50 paper (349 pp.). ISBN 978-0-19-856676-2, ISBN 978-0-19-856677-9 paper

One compelling reason to study statistical mechanics is the substantial insight it yields into an amazing variety of phenomena–-from the properties of black holes, to the organization of material inside human cells, to the behavior of financial markets. Another is its importance and centrality in many fields of physics: Statistical mechanics is typically a prerequisite to such courses as condensed-matter physics, astrophysics, and cosmology. Thus an important goal for an instructor teaching a course on the subject is to convey the range of applicability while presenting a fairly standardized curriculum.

James P. Sethna ‘s Statistical Mechanics: Entropy, Order Parameters, and Complexity does an admirable job of covering the fundamentals while also highlighting nontraditional areas to which statistical mechanics provides useful insights. Examples of applications in nontraditional areas are also presented throughout the text. Although the ordering of the material is nonstandard, in that random walks and diffusion are introduced before thermodynamics and partition functions, the choice of arrangement could be changed by the instructor, if desired. The material on random walks is used to good effect in the presentations on dynamical correlation functions and the concept of scale invariance. Thermodynamics is treated in parallel with partition functions, a choice that tends to mask the distinction between the properties that follow as a consequence of entropy being a state function and those that rely on how entropy is defined. The distinction, however, is not important in practical situations.

Sethna has made a series of thoughtful choices; the book is well organized and varied, yet not too long. It covers an appropriate selection of topics, and the amount of detail presented is suitable for an introductory course. The author has worked on many of the topics in the text; his experience is reflected in the interesting and cohesive perspectives related to the different subjects discussed and in the adaptation of calculations from his own work to new, substantial, and intriguing problems.

Each chapter has two short introductions: one to outline its contents and the other to discuss the exercises at the end of the chapter. The introductions are most useful for providing context, and they help the flow of the presentation. The one choice made by the author with which I disagree is that he did not provide literature recommendations when he did not cover a topic in depth.

A highlight of the book is the broad array of thoughtful exercises; an answer key to most of them is available to instructors on request. That sensible policy is a tremendous boon to time-crunched instructors who want to make up problem sets that take an appropriate amount of time for students to complete. Sethna asks that instructors do not post the answers to the exercises on the Web or distribute them electronically. The exercises include a substantial number of computational problems; software for several of them can be downloaded from the author ‘s website. Some of the software is prewritten so that students can easily download and run simulations. When I was writing this review, some of the canned exercises did not work on Macintosh OS X. I hope the problem is remedied by the time this review is published.

Some of the exercises in the book guide students to write their own simulations. They are encouraged to program in Python, a computer language that runs on all standard platforms and is relatively easy to learn. Some of the exercises would take a long time to grade, so it is best to assign them in a course only when the class is small or considerable grading assistance is available.

Sethna ‘s book provides an important service to students who want to learn modern statistical mechanics. The text teaches students how to work out problems by guiding them through the exercises rather than by presenting them with worked-out examples. Overall, Statistical Mechanics is probably more appropriate as a textbook than a self-study guide. Instructors can point out to students which material is core and central to understanding following chapters, and which is cultural and not required to comprehend later topics.