37
$\begingroup$

I learned thermodynamics and the basics of statistical mechanics but I'd like to sit through a good advanced book/books. Mainly I just want it to be thorough and to include all the math. And of course, it's always good to give as much intuition about the material.

Some things I'd be happy if it includes (but again, it mostly just needs to be a clear book even if it doesn't contain these) are:

  1. As much justifications for the postulates if possible, I'm very interested in reading more about how Liouville's theorem connects to the postulates.

  2. Have examples of calculating partition functions, hopefully not just the partition function for the ideal gas.

Improve this question
$\endgroup$
4
  • 2
    $\begingroup$ A good advanced book that covers in details and with mathematical rigor what you want and much more is Gallavotti's "Statistical Mechanics - a short treatise", which is not so short actually... You can get it from here. $\endgroup$
    – Yvan Velenik
    Commented Jun 21, 2012 at 20:07
  • 2
    $\begingroup$ Another good (but probably too advanced) book is the "old" book by Ruelle, "Statistical Mechanics - Rigorous Results". If you have the level in maths, and are interested in the mathematical theory of phase transitions for lattice systems, the classical reference is Georgii's "Gibbs measures and phase transitions" (although that's more graduate level stuff). $\endgroup$
    – Yvan Velenik
    Commented Jun 21, 2012 at 20:09
  • 1
    $\begingroup$ Just in case. Here are the google book pages for the last 2 refs, so that you can have an idea of what is done there and at which level: Ruelle, Georgii. $\endgroup$
    – Yvan Velenik
    Commented Jun 22, 2012 at 16:15
  • 2
    $\begingroup$ I just stumbled on this old question. As a complement to the previous comments, you could also look at this answer, in which I list many more mathematically rigorous references. $\endgroup$
    – Yvan Velenik
    Commented Aug 27, 2022 at 9:33

10 Answers 10

Reset to default
16
$\begingroup$

EDIT: My answer assumes that you're looking for a book at the introductory graduate level.

I found Pathria's "Statistical Mechanics" (2nd ed) very helpful during my first-year graduate statistical mechanics course. Pathria's treatment of the subject is mathematically careful and detailed, at least by physics standards; I found his discussion of Liouville's theorem (part 1 of your question) satisfactory. Unfortunately, like many formal treatments, Pathria discusses few interesting applications.

"Statistical Physics of Particles" by Kardar appears to be supplanting Pathria as the favored introductory graduate text; it was used at Boston University and at Caltech during my time there. Kardar is very terse and would probably have to be supplemented by another book, but the problems he offers are interesting (if hard). In fact, about a third of the text consists of detailed solutions to the problems.

I have heard good things about Reichl's book, already mentioned in another answer. I used it briefly as a reference: the coverage of kinetic theory is more complete than in other sources. It is more accessible than Pathria, not to mention Kardar.

Improve this answer
$\endgroup$
13
$\begingroup$

I recommend the book A Modern Course in Statistical Physics by Reichl. It starts with phenomenological thermodynamics, covers both equilibrium and nonequilibrium statistical mechanics, and discusses a wide range of applications, not only ideal and real gases. Its level of rigor is that of typical books on theoretical physics.

You may also be interested in my online book https://arxiv.org/abs/0810.1019 the part on statistical mechanics is nearly independent of the remainder.

Improve this answer
$\endgroup$
1
  • $\begingroup$ broken link, please update working link $\endgroup$
    – Saleem Ahmed
    Commented Oct 4, 2022 at 3:02
6
$\begingroup$

As an undergrad, we used "Thermal Physics" by Kittel and Kroemer:

http://www.amazon.com/Thermal-Physics-Edition-Charles-Kittel/dp/0716710889

Improve this answer
$\endgroup$
6
$\begingroup$

I recommend books by Kardar "Statistical Physics of Particles" "Statistical Physics of Fields" The mordern approach to this subject is helpful for your future study.

Also there are solutions to all of the problem, which you can find from the internet.

Improve this answer
$\endgroup$
5
$\begingroup$

Greiner's Thermodynamics and Statistical Mechanics is pretty good from a few short readings I did. Also, it has better reviews from almost all of the other popular textbooks on the subject in goodreads.com

Improve this answer
$\endgroup$
4
$\begingroup$

If anyone is interested in seeing how this is done from a chemist's perspective I can heartily recommend Statistical Mechanics: Theory and Molecular Simulation by Mark Tuckerman. Sadly, it isn't on line but can be ordered from Amazon or the like.

Improve this answer
$\endgroup$
1
  • $\begingroup$ this is an exeptionally good bok if your interested in getting a second look. (At least thats what I am using in it for) $\endgroup$
    – Kuhlambo
    Commented Feb 2, 2016 at 22:02
2
$\begingroup$

It has to be " Statistical Mechanics and Thermodynamics " by Claude Garrod". You can use the text by Macquarie as a supplement. For renormalization group and advanced concepts, use " Statistical Physics of Fields" by Kardar.

Improve this answer
$\endgroup$
2
$\begingroup$

It may sound old but 0."An introduction to statistical physics- by A.J. Pointon" is a very handy book to absorb the concept of calculation over phase space from the very beginning. The book is suitable for a one semester course, designed for last year undergraduate and beginning graduate students. The exposition of this book is exceptionally clear. It hardly skips any mathematics under the hood.

For more advanced treatment of the subject there are plenty of other good books. The list is not exhaustive at all..

  1. Statistical Mechanics, 2nd Edition by Kerson Huang
  2. A Modern Course in Statistical Physics 4th ( & 2nd) Edition by Linda E. Reichl
  3. Statistical Physics: Volume 5 3rd Edition by L.D. Landau, E. M. Lifshitz
  4. Statistical Physics of Particles 1st Edition by Mehran Kardar
  5. Statistical Mechanics 3rd Edition by R K Pathria, Paul D. Beale

One may also get interest into the book - 6. Introduction to Modern Statistical Mechanics 1st Edition by David Chandler. The approach of this book to the subject is very different than the above mentioned books.

Improve this answer
$\endgroup$
0
$\begingroup$

I'll assume that by advanced you mean advanced undergrad, the other answers seem to mix different level books.

I find that most advanced physics (not just stat mech) books range from bad to awful. Sadly, most standard books used on courses fall into this category, i see some of them in the other comments (like Greiner and Pathria).

Also, the two books i consider best are not mentioned in any of the comments.

Theory books

I'll list them from simplest to hardest.

  • Tong, Statistical physics lectures: Excellent for a first look on stat mech as an advanced undergrad. Free, available in the link. excellent prose. Good conceptual explanations. It covers all the basic results. For more advanced things or in depth, you'll need to consult other sources. Overall the best option.

  • Reif, Fundamentals of statistical and thermal physics: Not just good explanations, also makes you know which are the important things on each subject. Excellent prose, great conceptual explanations. A bit old. Excellent for most topics. The last part covers advanced kinetic theory, irreversible processes and fluctuations. I'd check this one when Tong's lectures are not enough.

  • Landau and Lifshitz, Statistical Physics: Volume 5: Just as Reif, it lets you know which things are important, but indirectly. Basically, if it isn't important, it's not in this book. The writing is excellent. Good explanations. Focus on central concepts. A lot of subjects are treated differently to standard books, usually simpler and relying more on physical grounds. Won't lose time over non important things. Almost every subject's simplest solution is found in this book. Too hard for humans. I'd take this one as the third option, unless you are well versed in the subject of interest.

One of your requests is:

Have examples of calculating partition functions, hopefully not just the partition function for the ideal gas.

For this, i'd recommend a special book only for examples:

Example books

Cini, Fucito and Sbragalia, Solved Problems in Quantum and Statistical Mechanics: lots of examples, it has 200 pages of solved problems in stat mech. Decent explanations, way better than other more known solved problems books, like Kubo or Dalvit.

Another request was:

Mainly I just want it to be thorough and to include all the math.

Greiner books

Greiner, Stöcker, Neise and Rischke, Thermodynamics and statistical mechanics: It is thorough in the math steps and it has a lot of examples for a theory book. Explanations are bad. Writing not good. Physical arguments and concepts nowhere to be found. Will treat the most important results (for example, the canonical/Boltzmann distribution) in the same way as the most superfluous details. Derivation of quantum statistics is specially bad. Usually I don't recommend it at all, but you may find it useful to check specific math steps or examples.

Improve this answer
$\endgroup$
0
$\begingroup$

If you know French, the way to go is:

  • Eléments de physique statistique by Bernard Diu, Claudine Guthmann and ‎Danielle Lederer.

The first author is the same co-author from the exemplary Cohen-Tannoudji's Quantum Mechanics series. It is very complete and with a lot of complementary chapters. It is sad that there is still no English version.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.