Statistical Mechanics: Entropy, Order Parameters and Complexity (Oxford Master Series in Physics) [Paperback]

I haven't yet had a chance to read this book from cover to cover. However, after several hours with it, some of its strengths and weaknesses became evident. Many of these complement each other.

It covers an exciting range of contemporary applications -- take a look at the table of contents. The problems are long, discursive, and even more intriguing than the main text, covering topics like the cosmic microwave background, origami microstructures, Langevin equations, snowflakes, biochemical reaction rates and NP-completeness. The book is rich in illustrations, and in footnotes that give an informal commentary on the main text.

One downside is that, being so wide, the coverage is also a bit thin in places. Many of the most interesting contemporary topics, such as the statistical mechanics of networks, are covered *only* in exercises. Thermodynamics is dismissed in less than 10 pages in the middle of the book, owing to that subject's being "cluttered" with a "zoo of partial derivatives, transformations and relations."

The exercises look to be more fun and tempting than usual in books on this subject. So it's a definite bummer that the book neither includes answers or hints, nor states problems in closed form ("Show that this stuff = X"). The book's web site contains only some hints for computational exercises, plus a bunch of additional problems (again, without answers). If you're interested in self-study, this tease is frustrating - an automatic one-star deduction.

There's more good news/bad news with the author's aim to be relevant to fields outside traditional physics -- e.g. in econophysics and social science. This certainly makes the book up-to-date and attractive, and was one of the reasons I bought it. But applying physics to social science is a tricky business. There's a couple hundred years of failed attempts, because people blithely modeled stuff without thinking enough about the limits within which such an analogy might be appropriate. And many who do think about those limits when deriving a model often forget about them when applying it.

An example is the Black-Scholes model of option pricing. The model's results are "simply wrong" (B. Mandelbrot). Its assumptions about volatility and the structure of the option contract aren't empirically justified. Its blind application contributed to the 1987 stock market break. And the investment fund run by one of its Nobel-laureate inventors went bust in flames in 1998. In this book, there's an exercise that walks you through some of the underlying concepts of Black-Scholes (pp. 32-33). But the author only praises the model, without so much as a footnote mentioning its darker side.

Even when doing "traditional" physics, one ignores philosophical issues at one's peril. A lot of the great physicists of the past century weren't being stupid to fret over them. On the other hand, there are lots of folks like my QM professor in the 1970s, who explained that the only reason Bohr, Heisenberg and Einstein discussed philosophy was that they didn't understand QM, "but today we understand it very well, so we don't need to worry about that stuff."

Unfortunately, this book continues that gung-ho, what-me-worry tradition. A disappointing example is the discussion of information and entropy (pp. 85 ff). The author states that interpreting entropy "not as a property of the system, but of our knowledge of the system ... cleanly resolves many otherwise confusing issues" (@ 85). This "cleanly" is a bit disingenuous, since plenty of people wouldn't agree with this interpretation (see, e.g., J. Bricmont's 1995 paper "Science of Chaos, or Chaos in Science?", available on the arXiv). The discussion of the arrow of time (pp. 80-81) does mention a couple of nuggets of relevant history, but the level of treatment is more suitable for a pre-med physics survey class than for a graduate course in stat mech.

A couple of pages later (pp. 87-90), the author slides from a discussion of Shannon entropy to discussing an algorithm for helping your roommate find her keys by asking her questions. Without acknowledging it, he introduces the notion of meaning into "information" -- but meaning wasn't relevant for Shannon. Indeed, the historical background for why Shannon called his quantity "entropy" -- John von Neumann advised him to use the term because "nobody understands entropy" -- suggests one should be very cautious about mashing up the various scientific and colloquial meanings of "information".

It's just this kind of unreflective enthusiasm when applying physics techniques outside their usual domain that leads to so many junk "Physics and Society" papers on the arXiv. At least one-half star deduction, for an upper bound of 3.5 stars.

NOTE ADDED 2007/03/27: I recently received a very gracious email from the author addressing some of the above comments. I wasn't convinced by him about Black-Scholes or entropy (which he claimed to understand "in the broad context" better than Claude Shannon or J. Bricmont), but I do appreciate his engaging me on those points. He's also prepared an answer key to the exercises, though you'll need to write to him and convince him that you aren't taking the course for credit before he'll send them to you. (In my case my review apparently was credible evidence enough; not sure what it might take in yours, but from his note it sounds like it's not an impossible task.) I can't say that this materially changes my rating of the book, but I certainly give five stars to the author for his sincerity.

The book Statistical Mechanics: Entropy, Order Parameters and Complexity by James Sethna is excellent. I have used it as the main textbook in my course on Statistical Physics for first year graduate students at the Universidade Estadual de Campinas (UNICAMP) in Brazil. The students and I liked it very much.

I think that the main quality of the book is that it presents Statistical Physics as a very dynamical subject, interconnected with several subjects within physics, as well as outside it.

Since the book is aimed for a one semester course on the subject, the author had to make important choices. I really liked his choices. For instance, the book does not discuss approximate methods used to treat systems with interacting particles, instead the author has chosen to have a chapter on Calculation and Computation. Although these methods have played an important role in the past, nowadays the study of the relevant problems in the field require computer simulations. The chapter on Computer Simulation is excellent. Instead of only discussing how to perform a Monte Carlo simulation, it proofs mathematically in detail (except for the Perron-Frobenius theorem) why one ends up with an equilibrium probability distribution after a number of Monte Carlo steps. Another important subject covered in the book is that of Abrupt Phase Transitions. For most Statistical Physics books, only Second Order or Continuous Transitions exist. The exercises are also another very important and interesting choice made by the author. They are very different from the usual exercises one can find in a regular textbook on Statistical Physics. The exercises are in general very intelligent and they appear in a broad range of difficulty, from those which can be solved by inspection to those that are small projects. I recall two great examples, exercises 5.7 and 5.10, where it is shown in a very clear and clever way that, when we know the system from a microscopic point of view, its entropy does not increase, whereas if we know only a coarse-grained description of it, then its entropy does increase. Some exercises lead the reader, in a secure way, through aspects of the theory that are not covered in the text. For instance, Landau's theory for phase transitions is presented in a very nice way in exercise 9.5.

Perhaps, the aspect that I have enjoyed most in the book is that the author does not shy away from discussing one of the thorniest points in the fundamentals of Statistical Physics: what entropy really is. The book discusses in some detail Phase Space Dynamics and Ergodicity. It presents some physical situations where the ergodic hypothesis breaks down. Usually this problem with the theory is swept under the rug in most textbooks. One very interesting case is that of the entropy of glasses. A subject the author himself has worked on. If a liquid is cooled down very fast it may become a glass, undergoing what is called a glass transition. When the system is in the liquid phase its atoms are diffusing and the system goes through all different possible configurations, that is believed to be the cause for its entropy (ergodicity). When the liquid undergoes a glass transition, the atoms cease diffusing and the system is jammed in one (a single one) structure of the liquid that generated it. If the system is not anymore going through all the possible configurations available what has happened to its entropy? No heat is released in this transition, therefore, one does not expect a change in its entropy. A hardcore purist would answer that the glass is not a system in equilibrium and, therefore, the entropy is not well defined. The point is, it may take much more than the age of the Universe for the glass to reach the final equilibrium and become a crystal (reported changes in glasses of ancient churches are urban legends). The question about what has happened to the entropy of the liquid remains there, despite the purist's answer. The experimentalists can measure very well the residual entropy of a glass. For the author, for me and fortunately nowadays for many others, the satisfactory answer is that the entropy of a glass is the missing information about the system. Another example of residual entropy can be found in the ice cubes in your refrigerator.

At last but not least, I would like to comment on a misconception of a previous reviewer about Shannon's Information Theory. The entropy proposed by Shannon is a measure of the uncertainty of a set of possible messages that can be exchanged, regardless the content of each message. Therefore, this entropy is related to the probability distribution associated with the ensemble of possible messages, regardless of their content. If there are any doubts, I would suggest reading the first chapter of the book Mathematical Foundations of Information Theory by A. Ya. Khinchin. In section 5.3.2 of the book, the author is just analyzing the properties of the Shannon entropy of a probability distribution using a humorous example. The probability distribution can be associated with anything, even with a key lost by a careless room-mate. This entropy is a property of the probability distribution, independent of any possible meaning attributed to it by a human being.

I immensely enjoyed studying this statistical mechanics book. I think that the author, James Sethna, has a "Feynman-like" ability to explore his subject matter with much depth, insight, and many playfully creative excursions. The exercises cover such topics as the thermodynamics of Dyson Spheres and black holes; of how many shuffles it takes to fully randomize a card deck; and of whether an advanced, intelligent being or civilization can, from a thermodynamic standpoint, manage to process an infinite number of thoughts before the heat death of the universe, or whether they are limited to a finite number of thoughts. I think that there is a lot of wisdom and insights in this book which is missing in other books I've read on statistical mechanics and thermodynamics, where I often feel overwhelmed by a zoo of partial derivatives and thermodynamic equations with little guidance given on how the entire structure fits together. I strongly recommend this book for anyone who has studied some statistical mechanics and/or thermodynamics in a lower-level undergraduate course, and is looking for more advanced upper-level undergraduate or graduate-level text.