Customer Reviews

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

5 star:		(6)
4 star:		(2)
3 star:		(1)
2 star:		(1)
1 star:		(1)

 

 

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.

This books is reader friendly and very interesting. In the chapter about correlation function & linear response theory, the demonstration is very clear and self-consistent. As a student who is new to this topic, I think this chapter is even better than Chandler's book on this topic( I love Chandler's intro too). The problem set seems to be stimulating and may need more time than learning the main text. And more, the appendix is on Fourier Transform, a saver to the chemistry student like me.

This book is an excellent introduction to extremely relevant modern topics in statistical mechanics. I found this book, along with the author's course website, to be an excellent resource for self-teaching. My background: I have a PhD in biochemistry, my research field is systems biology, and I've never had a formal stat mech course. What makes this book outstanding is the somewhat unorthodox format for a textbook: an excellent selection of topics for text make up about half of the book, and the other half is comprised of lengthy, well-crafted problems that teach and reinforce core concepts, as well as demonstrate some very interesting applications in a variety of fields including computation, biology, pure math, physics, and finance. As a bonus, the bibliography is filled with some real gems that are worth looking up.

This is not a comprehensive reference book. It's great for learning, but if you need a book with more in-depth discussions or derivations for later reference, it's probably handy to also have a more standard textbook - for my purposes, I use Terrell Hill's Introduction to Statistical Thermodynamics alongside Sethna's Statistical Mechanics.

One final point: This book has influenced my teaching philosophy. Teaching concepts through a few long, well-designed problems seems more effective than lengthy exposition followed by piles of short, drill-like problems.

I came across this almost by accident, but it is a really nice book. You don't often get to see authentic disciplinary speciation, but currently, it looks as if something like speciation is happening with the hybrid of statistical mechanics and a certain flavour of computer/computational science (two different things) and information theory. Hence books like this, or David MacKay, or Mazard and Montanari, or..., all of which are serious theoretical books written by professors of theoretical physicists, but which are clearly wandering off from the concept of a theoretical _physics_ book, even if they equally clearly all start from a basis in stat-mech (I was interested to see, when I looked up Mazard, for instance, that Amazon asked me if I would like to buy it together with Koller and Friedman's book on graphical models, not with a another physics book - Sethna seems to be more exclusively bound to other physics books than I would have expected). Unlike MacKay, Sethna is still clearly a genuine theoretical physics book, but it isn't your father's stat-mech book (for that, see Reif or Landau or something).

Anyway, it's great. But, note, if you _are_ looking for something like Reif or Landau, then this may not be what you are looking for. Also, you'll have to do the exercises.

I'm studying for my final physics exams and - after having a look at a half-dozen or so other statistical mechanics book in the library - (none got me really involved) I have just to say that I'm really glad that I decided to buy this book!
It's really a joy and fun to read! I think that the other reviewers already gave a good description of the book and about the exercises I can confirm that there are lots of them with many topics being covered there. I personally think this is good, specially for self study - better do-it-yourself, the majority of them are very well elaborated and interesting.
I only wish also that some solutions would have been provided... (although I guess all of them together would fill another 300 pages book);
In any case highly recommended!

This advanced undergraduate or introductory graduate level text on statistical mechanics is clearly written by a master and perhaps visionary teacher. Statistical mechanics remains, in my opinion, the only truly rigorous science of emergent phenomena. As the scientific community in general focuses more on complex systems, it is likely that the techniques developed for the theoretical study of the statistical thermodynamic properties of matter will find widespread applications from biology to banking. In this spirit, this book is written to educate the next generation of scientists rather than as a text focused solely on existing applications.

While the subject matter of this book easily devolves into mathematical gymnastics, this text is wonderfully written to simultaneously build up an intuitive grasp along with proficiency with mathematical concepts. Introductory chapters on "What is statistical mechanics?" and "Random walks and emergent properties" are deceptively simple: the mathematical techniques employed in these chapters should be immediately accessible to senior level physics and engineering students. Yet by the end of Chapter 2, one finds oneself deriving a simple one-dimensional Fokker-Planck equation--a nontrivial application in statistical mechanics with applications in chemical kinetics, transport phenomena, mathematical biology, and finance.

This appeal to potentially broad applications is part of what makes this book unique. While a great number of important physical concepts are developed, this is really not an ordinary physics book. Instead, the tools and techniques of statistical mechanics are developed from an exceptionally broad perspective.

While I have worked very few of the problems, the end-of-chapter problems sets present deep and detailed questions that are critically integrated into the text. A reader who has the time and dedication to do the problems will gain much more than one who does not.

Overall, this is not a really bad book, the problem is the text is really short on explanations, and has virtually no examples. The author assumes that most of the learning will be done through the problems. Problem is most people don't have that kind of time to waste with problems.

If you like working problems, this is the book for you, if you want an informative text, than this is definitely not the book for you.

I really would like an updated version of Kerson Huang's truly excellent text. Statistical Mechanics, 2nd Edition

This book is good only if you already know the subject from other books (like Donald Macquire or Pathria).