General textbook comparison thread

Two excellent recent textbooks on statistical mechanics (well, three really, but two of them are better considered different volumes of the same text):

• Statistical Mechanics: Entropy, Order Parameters and Complexity by James Sethna. Available for free download here.

• Statistical Physics of Particles and Statistical Physics of Fields by Mehran Kardar.

Sethna gives a very unorthodox presentation of the material, focusing more attention on exciting new developments in condensed matter physics than other texts at the same level and (I think correctly) de-emphasizing thermodynamics. He treats statistical mechanics as an interdisciplinary field of study rather than just a branch of physics, and this is an ideal text for people interested in the application of statistical mechanical tools to economics, computer science, cosmology, population biology, and many other sciences given short shrift in more traditional treatments. Sethna is an excellent writer and the book is not too techical, so it is great for self-study. The book also has the most impressive set of exercises I have ever seen in a physics text. The exercises are detailed, explore a huge variety of topics, and are a joy just to read through even if you don't intend to solve them. The text does sacrifice depth for breadth. While most important topics in statistical mechanics are discussed somewhere in the book, they are often not treated with a high degree of rigor. The book is extremely enlightening if you want a broad overview of the techniques and achievements of contemporary stat. mech., but if you are looking for, say, a careful derivation of Boltzmann's equation, this is not the place to look. The text should be accessible if you have a solid grasp of calculus, basic statistics and intermediate classical mechanics. Some sections presuppose knowledge of quantum mechanics.

Kardar's text is more technically demanding and more of a slog to read than Sethna's. It is, however, the most lucid presentation of the material I have yet encountered. Kardar develops the subject carefully and rigorously, filling in conceptual gaps that are traditionally left unaddressed. I am writing a dissertation on statistical physics, so I consider myself very familiar with the field, but I still learned a huge amount from reading Kardar. There were many places where he presented material I had previously encountered in a novel manner that finally made things click. The first volume of his text covers thermodynamics and traditional single-ensemble topics in stat. mech. The second volume discusses scaling and renormalization, and is by far the best introduction to these topics I have ever read. Kardar includes a number of very interesting problems (although not quite as interesting as Sethna's), and many of them are solved. The text is at the graduate level, but I think it can be tackled by a motivated upper-level undergraduate.

Which one of these books would I recommend? It depends on what you're looking for. If you're not a physicist and want a fairly advanced introduction to statistical mechanics, Sethna is the way to go. He covers a broader range of topics, is less focused on training physicists, and is a more entertaining read. If you have studied stat. mech. at an undergraduate level and want a more rigorous understanding of the fundamentals, or if you're really interested in the foundations of the discipline rather than its myriad applications, I would recommend Kardar. If you're fairly new to stat. mech. and want to develop an understanding of the field that will allow you to tackle the professional literature, read Sethna first, then Kardar.

I'll bite: Two textbooks on the level of upper-division undergraduate physics for classical dynamics that I've read are:

• Classical Dynamics of Particles and Systems by Thornton and Marion

• Classical Mechanics by John Taylor

Both cover roughly the same material, but Taylor gives an introduction to fluid mechanics equations in one of the later, optional, chapters that I believe Thornton and Marion do not cover. Thornton-Marion covers gravitation and theory of scalar potentials better.

The two books differ mainly in the way that they present the material. Taylor is very straightforward, easy to understand, and has clear examples with helpful diagrams. Thornton-Marion is very mathematical, requiring at times taking a break to derive a formula in order to follow the discussion. Thornton-Marion is in general less clear for a first read-through or an attempt to refresh if understanding is cloudy, but it excels in the problem sets and worked examples; the problems are very challenging and working through them is a good way to develop an understanding of the material. Taylor's problems are adequate, but they are not as difficult as Thornton-Marion's and feel more like textbook problems than the open-ended problems of T-M that are more like what a physicist would encounter.

All in all, however, I would heavily recommend Taylor over Thornton-Marion. It is simply much, much, clearer, gives a better understanding of the topic, and is a pleasure to read. This is especially true if you are learning about the topic for the first time! Thornton-Marion could be useful for studying if you work through problems and have the solutions manual for checking them. If you already know the material well, T-M might be better as a concise reference guide, but Taylor is not shabby as a reference if you know what you are looking for.