Opinions on books for (self) studies in statistical physics

[ipsky]

Nearly two decades after I graduated with an engineering degree, I'm currently studying for a master's with a particular emphasis on conceptual/theoretical statistical physics. Based on my interests and stylistic preferences, I'm using the following books to build my understanding of physical mathematics. However, since I lack a formal bachelor's degree in physics, I'm not certain if I'm missing out on crucial insights from 'new' physics taught at bachelor's level today. What I'm looking for are informed opinions about these books: whether they fall short or diverge from the state-of-the-art so significantly so as to limit their use as textbooks, and if they do, their suitable alternatives.

G. Joos and I. Freeman, Theoretical physics, 3 ed. (1958).
A. Kompaneyets (trans. G. Yankovsky), Theoretical physics (1961).
L. Landau, E. Lifshitz and L. Pitaevskii, Statistical physics (part I), 3 ed. (1980).
B. Lavenda, Statistical physics, A probabilistic approach (1991).
N. Piskunov (trans. G. Yankovsky), Differential and integral calculus (I and II) (1978).
B. Gnedenko (trans. G. Yankovsky), The theory of probability (1978).
R. von Mises and H. Geiringer, Mathematical theory of probability and statistics (1964).

 

[Dr Transport]

start with "baby Reif" in the Berkeley series.

https://www.amazon.com/dp/0070048622/?tag=pfamazon01-20

 

[vanhees71]

Nearly two decades after I graduated with an engineering degree, I'm currently studying for a master's with a particular emphasis on conceptual/theoretical statistical physics. Based on my interests and stylistic preferences, I'm using the following books to build my understanding of physical mathematics. However, since I lack a formal bachelor's degree in physics, I'm not certain if I'm missing out on crucial insights from 'new' physics taught at bachelor's level today. What I'm looking for are informed opinions about these books: whether they fall short or diverge from the state-of-the-art so significantly so as to limit their use as textbooks, and if they do, their suitable alternatives.

G. Joos and I. Freeman, Theoretical physics, 3 ed. (1958).

It's a marvelous book, but in some parts a bit outdated (particularly quantum mechanics).

A. Kompaneyets (trans. G. Yankovsky), Theoretical physics (1961).

This I don't know.

L. Landau, E. Lifshitz and L. Pitaevskii, Statistical physics (part I), 3 ed. (1980).

The entire Landau-Lifshits series is a masterpiece; this vol. V is among the best statistical-physics books I know. It's definitely graduate rather than undergraduate level.

B. Lavenda, Statistical physics, A probabilistic approach (1991).
N. Piskunov (trans. G. Yankovsky), Differential and integral calculus (I and II) (1978).
B. Gnedenko (trans. G. Yankovsky), The theory of probability (1978).
R. von Mises and H. Geiringer, Mathematical theory of probability and statistics (1964).

These I don't know.

For statistical physics I'd recommend to start with the Berkeley Physics Course volume on the subject (the "little Reif") or Becker, Theory of Heat.

 

[Mondayman]

The new edition of An Introduction to Thermal Physics by Schroeder looks like a well written introductory book from I've glanced at. I haven't started studying from it yet, however.

 

[ipsky]

start with "baby Reif" in the Berkeley series.

https://www.amazon.com/dp/0070048622/?tag=pfamazon01-20

Thanks! I was not aware of this introductory text, and will look it up. I have been referring his textbook and definitely find it suitable.

 

[ipsky]

The entire Landau-Lifshits series is a masterpiece; this vol. V is among the best statistical-physics books I know. It's definitely graduate rather than undergraduate level.

Thank you for the information. It takes many readings of Landau-Lifshitz for me to understand the concepts, but I enjoy it that way. The only other book from the series I have browsed so far is vol. 1 (mechanics). Alexander Kompaneyets' book on theoretical physics feels to me like a condensed version of the Landau-Lifshitz series which is not surprising as he was Landau's student.

 

[ipsky]

I'm satisfied with the content and difficulty level of the books I have listed. Since most of them have been written many decades ago, I only wish to know if there are any clear discrepancies in them with regard to current physics. Much like what @vanhees71 has mentioned of Joos' book.

 

[ipsky]

The new edition of An Introduction to Thermal Physics by Schroeder looks like a well written introductory book from I've glanced at. I haven't started studying from it yet, however.

Thanks, will take a look.

 

[madscientist_93]

I think starting with Berkely Physics series : Statistical Physics is a good idea as recommended by @Dr Transport . Richard Becker's Theory of Heat recommended by @vanhees71 is a classic as well but I think it uses CGS units. In addition to the other recommendations in the thread I recommend the works of Peter T Landsberg :

1. Thermodynamics and Statistical Mechanics ( 1990 Dover Publications )
2. Problems in Thermodynamics and Statistical Physics ( 1971 Pion Limited )

Both of these books come with detailed solutions suitable for a self learner.

 

[paralleltransport]

Nearly two decades after I graduated with an engineering degree, I'm currently studying for a master's with a particular emphasis on conceptual/theoretical statistical physics. Based on my interests and stylistic preferences, I'm using the following books to build my understanding of physical mathematics. However, since I lack a formal bachelor's degree in physics, I'm not certain if I'm missing out on crucial insights from 'new' physics taught at bachelor's level today. What I'm looking for are informed opinions about these books: whether they fall short or diverge from the state-of-the-art so significantly so as to limit their use as textbooks, and if they do, their suitable alternatives.

G. Joos and I. Freeman, Theoretical physics, 3 ed. (1958).
A. Kompaneyets (trans. G. Yankovsky), Theoretical physics (1961).
L. Landau, E. Lifshitz and L. Pitaevskii, Statistical physics (part I), 3 ed. (1980).
B. Lavenda, Statistical physics, A probabilistic approach (1991).
N. Piskunov (trans. G. Yankovsky), Differential and integral calculus (I and II) (1978).
B. Gnedenko (trans. G. Yankovsky), The theory of probability (1978).
R. von Mises and H. Geiringer, Mathematical theory of probability and statistics (1964).

I know landau lifshitz vol. 5. It's a beautiful book and everything in there is done well. However, it covers an overwhelming number of topics (including chemical kinetics) which most undergraduates in physics don't study. This is classic landau.

Your question puzzles me: why would you restrict your studying to old books? My personal preference for statistical physics is Kardar vol. 1 & 2. It's more modern than landau and short enough for self study. It also covers kinetic theory and probability as its foundation from the start (landau series has a beautiful discussion of Boltzmann H but only on vol. 10).

Furthermore, this is a very large number of books, and some are very elementary (I assume you already know calculus/probability otherwise you wouldn't even be able to start landau).

 

[robphy]

The new edition of An Introduction to Thermal Physics by Schroeder looks like a well written introductory book from I've glanced at. I haven't started studying from it yet, however.

From https://physics.weber.edu/thermal/ ,

New publisher! I am delighted to announce that
An Introduction to Thermal Physics
is now published by Oxford University Press.
It is available in hardcover (ISBN 978–0–19–289554–7), paperback (ISBN 978–0–19–289555–4), and ebook (see below) formats.
...

Except for about three dozen new page corrections ( https://physics.weber.edu/thermal/corrections.html ) , the OUP reissue is identical in content to the Pearson version.

As an undergraduate student, I did not enjoy, understand, or appreciate statistical mechanics.
As an instructor/professor, I was given the opportunity to teach it...
... and I chose Schroeder's text since it was commonly used textbook.
I have a better appreciation and understanding of the subject.
It was helpful to read
"A different approach to introducing statistical mechanics" (1997)
Thomas A. Moore, Daniel V. Schroeder
https://arxiv.org/abs/1502.07051
( Am. J. Phys. 65 (1), 26-36 (1997) : https://doi.org/10.1119/1.18490 )
Also see Unit T of Tom Moore's Six Ideas that Shaped Physics
http://www.physics.pomona.edu/sixideas/ .

 

[ipsky]

Furthermore, this is a very large number of books...

That is part of the problem! The developments in statistical physics over the last five decades, it seems to me, have only led to diverse applications and not to clarity in the foundations itself. The modern textbooks on the subject neither explore the new applications thoroughly nor expound the foundations satisfactorily. The only exception I have come across are S-K Ma's Modern Theory of Critical Phenomena and Statistical Mechanics. The books I have listed in my original post suffice, as they are a very clear exposition on the foundations. They are not hard to follow as long as I'm patient enough. What I'm looking for are suggestions on books that describe the new applications without muddling the foundations.

 

[paralleltransport]

That is part of the problem! The developments in statistical physics over the last five decades, it seems to me, have only led to diverse applications and not to clarity in the foundations itself. The modern textbooks on the subject neither explore the new applications thoroughly nor expound the foundations satisfactorily. The only exception I have come across are S-K Ma's Modern Theory of Critical Phenomena and Statistical Mechanics. The books I have listed in my original post suffice, as they are a very clear exposition on the foundations. They are not hard to follow as long as I'm patient enough. What I'm looking for are suggestions on books that describe the new applications without muddling the foundations.

Maybe I'm confused but most of your books don't deal with the foundations of stat mech but basic math prerequisites to do undergraduate physics (differential/integral calculus, probability for example).

I assume your interest is equilibrium stat mech (non-equilibrium is a whole different beast).

Which part of the foundations do you think is inadequately addressed? Kardar vol. 1 starts from basic probability to Boltzmann H theorem (which justifies why anyone would care about equilibrium stat mech) in about 50 pages. In my book, if you can start from basic probability -> Boltzmann H -> microcanonical ensemble, you've checkmated the foundations.

The last 50 years have seen very interesting understanding of equilibrium stat mech of interacting systems, which I would consider foundational. This is what you referred to as the theory of critical phenomena and is addressed by a statistical physics of fields book (S.K. Ma, kardar vol. 2, zinn-justin's, and many others). I would just not pick any book < 1970 to study critical phenomena, since it was worked out by wilson around 1970.

Since you are self-studying, kardar's 2 semester stat mech lecture course is available on ocw.

 

[mpresic3]

I only wish to know if there are any clear discrepancies in them with regard to current physics.

In my opinion of the first three books you list, I am familiar with. They seem to be well chosen, for physical mathematics. I do not know of any clear discrepancies. Moreover, many times the older textbooks are very good, and better than the present ones. Core physics (physics necessary to start conducting research, (e.g. physics required to pass qualifyifying exams at competitive universities ) does not change much over the last 50 years.

You can always catch up later with modern developments once your core is set. For example, I find the earlier version of Goldstein, without the chapter on Chaos Theory, better. If one wants to learn chaos theory, it is best to study a textbook that treats the subject separately. I have read other opinions in the physics forum that suggests the textbooks that treat non-relatvistic quantum theory often contain a chapter or two on relativistic quantum theory, but they are better treated in specialized textbooks.

 

[Mr.Husky]

I don't know about statistical mechanics. But for classical thermodynamics, Enrico fermi's little book is great. I also found the following book very interesting:-https://www.amazon.com/dp/0521274567/?tag=pfamazon01-20

 

[vanhees71]

You can always catch up later with modern developments once your core is set. For example, I find the earlier version of Goldstein, without the chapter on Chaos Theory, better. If one wants to learn chaos theory, it is best to study a textbook that treats the subject separately. I have read other opinions in the physics forum that suggests the textbooks that treat non-relatvistic quantum theory often contain a chapter or two on relativistic quantum theory, but they are better treated in specialized textbooks.

The newer edition of "Goldstein" (spoiled by other authors, who didn't dare to write their own textbook instead) is definitely worse than the 2nd edition (see the discussions about their wrong treatment of nonholonomous constraints using the Hamiltonian principle and then not even realizing that they contradict themselves compared to the correct treatment with d'Alembert's principle).

I'd omit anything titled "relativistic quantum mechanics", because it's highly confusing. It's the idea to just write down the Dirac equation instead of the Schrödinger equation and claiming the physical interpretation was as in non-relativistic quantum mechanics as a single-particle description. That's really outdated, because today we know that particles can always be created and destroyed in scattering events at relativistic energies, i.e., the physically meaningful treatment is in terms of relativistic quantum field theory. The old-fashioned realtivistic quantum mechanics can be worked out as Dirac did for QED in terms of "hole theory" (i.e., filling up the negative-frequency states with electrons, claiming they were unobservable and only holes in this "Dirac sea" describe positrons). Admittedly that's at the end equivalent to modern QED but much more cumbersome to understand an use. Here, I'd recommend modern textbooks like Schwartz or Peskin&Schroeder (being aware of the many typos). The definitely best treatment is by Weinberg's 3 volume book + Duncan's book (The conceptual framework of quantum field theory) elucidating some aspects left out by Weinberg (like Haag's theorem and why "one doesn't need to worry about it").

 

[ipsky]

Maybe I'm confused but most of your books don't deal with the foundations of stat mech but basic math prerequisites to do undergraduate physics (differential/integral calculus, probability for example).

Are you familiar with any of the books, other than Landau's, that I have listed? All of them describe the foundations of statistical physics, albeit with differing points of view and levels of detail. Probability theory, is in my opinion, is at the heart of this foundation. The books on calculus by Piskunov contain excellent treatment of techniques required for studying both equilibrium and non-equilibrium phenomena.

Which part of the foundations do you think is inadequately addressed?

Usually it is the relation between thermodynamic probability, statistical probability and theory of errors. I have understood Boltzmann's work better when it is derived from probabilistic reasoning and not using kinetics. This requires much more than basic probability. The H-theorem then is the natural consequence of statistical regularity, and equilibrium thermodynamics is a limiting case. Modern books I have browsed through discuss none of this. But I could be mistaken.

I would just not pick any book < 1970 to study critical phenomena, since it was worked out by wilson around 1970.

My original post was precisely this. I'm looking for recommendations on what 'modern' textbooks I can refer to complement what is missing from the books I have listed, that include, for example, new developments in the study of critical phenomena. But I have not found any modern books except S-K Ma's that provide what I'm looking for. Landau's book covers some aspects of phase transitions.

Since you are self-studying, kardar's 2 semester stat mech lecture course is available on ocw.

I'll browse through it, thank you.

 

[paralleltransport]

Are you familiar with any of the books, other than Landau's, that I have listed? All of them describe the foundations of statistical physics, albeit with differing points of view and levels of detail. Probability theory, is in my opinion, is at the heart of this foundation. The books on calculus by Piskunov contain excellent treatment of techniques required for studying both equilibrium and non-equilibrium phenomena.Usually it is the relation between thermodynamic probability, statistical probability and theory of errors. I have understood Boltzmann's work better when it is derived from probabilistic reasoning and not using kinetics. This requires much more than basic probability. The H-theorem then is the natural consequence of statistical regularity, and equilibrium thermodynamics is a limiting case. Modern books I have browsed through discuss none of this. But I could be mistaken.My original post was precisely this. I'm looking for recommendations on what 'modern' textbooks I can refer to complement what is missing from the books I have listed, that include, for example, new developments in the study of critical phenomena. But I have not found any modern books except S-K Ma's that provide what I'm looking for. Landau's book covers some aspects of phase transitions.I'll browse through it, thank you.

I know the book by piskunov. It's a soviet era calc I-III textbook. I don't see any stat mech in there.
The book by gnedenko is a very old basic probability textbook (no measure theory). There are many equivalents that are more concise (sheldon ross's book for example). You get to characteristic functions only in p. 250, the central part for stat mech. Kardard gets you to characteristic functions in 10 pages into his probability chapter.

My understanding is most modern stat mech books derive the different ensembles as the entropy maximizing distribution (under various constraints). The reason for this is Boltzmann H theorem which states that entropy is monotonic increasing for "typical" assumptions about the collision processes. I don't see a major problem with that approach but maybe I'm ignorant of the subtle issues.

The probability & statistics needed to then study stat mech is basics about moment/cumulant generating functions, and large N approximations (stirling, CLT). All this is covered in Kardar vol. 1. Regarding probability being central to stat mech, I agree. It's very straightforward, all covered in ch. 3 of kardar (he has a chapter on probability). Surprisingly landau doesn't do as much probability which is why I prefer kardar.

 

[ipsky]

My understanding is most modern stat mech books derive the different ensembles as the entropy maximizing distribution (under various constraints). The reason for this is Boltzmann H theorem which states that entropy is monotonic increasing for "typical" assumptions about the collision processes.

I came through to the maximum entropy hypothesis from probability and information theory, and ergodic hypothesis. Using ergodicity and the concepts of extensive and intensive quantities, I have come to understand some foundations of equilibrium and non-equilibrium mechanics. The concept of ensembles appears to me as vestigial rather than fundamental. And most modern books appear to be ensemble heavy. Am I mistaken?

The probability & statistics needed to then study stat mech is basics about moment/cumulant generating functions, and large N approximations (stirling, CLT). All this is covered in Kardar vol. 1.

I had consulted the chapter on kinetic theory of gases from his book (vol. 1), and I found it hard to follow. I could not detect the physical significance of the concepts from the text. Perhaps it is designed for those who take his courses, or follow his videos online. I'll browse through Kardar's videos.

As my previous degrees have been in engineering, I have not had the chance to study physical mathematics in sufficient detail. If you consult my original post carefully, you will see that the book list covers 'physical mathematics'. All except Piskunov's cover at least some, if not all, aspects of statistical physics. I have been using Piskunov to refresh my mathematics skills, and it does contain very useful tools necessary for studying statistical physics. I'm very satisfied with all of these books. But I'm not knowledgeable enough to know whether they are sufficient and relevant enough for doing physics today. Hence the post!

 

[paralleltransport]

I came through to the maximum entropy hypothesis from probability and information theory, and ergodic hypothesis. Using ergodicity and the concepts of extensive and intensive quantities, I have come to understand some foundations of equilibrium and non-equilibrium mechanics. The concept of ensembles appears to me as vestigial rather than fundamental. And most modern books appear to be ensemble heavy. Am I mistaken?I had consulted the chapter on kinetic theory of gases from his book (vol. 1), and I found it hard to follow. I could not detect the physical significance of the concepts from the text. Perhaps it is designed for those who take his courses, or follow his videos online. I'll browse through Kardar's videos.

As my previous degrees have been in engineering, I have not had the chance to study physical mathematics in sufficient detail. If you consult my original post carefully, you will see that the book list covers 'physical mathematics'. All except Piskunov's cover at least some, if not all, aspects of statistical physics. I have been using Piskunov to refresh my mathematics skills, and it does contain very useful tools necessary for studying statistical physics. I'm very satisfied with all of these books. But I'm not knowledgeable enough to know whether they are sufficient and relevant enough for doing physics today. Hence the post!

I don't know what is considered "vestigial" or "fundamental". Here's how I was taught:
At a elementary level, all the ensembles are just entropy maximized distributions for the microstates of the system, with different constraints. The reason why they all give the same answers in the large sample size limit is explained in any grad stat mech textbook and is a consequence of CLT (cartoon level explanation). The fact they give the same answer means you just pick the ensemble that makes calculation easiest.

Why ensembles are entropy maximizing?

At an undergraduate level, the fact "stuff" maximizes entropy is assumed using some heuristics. At a graduate level like kardar, this is proven to be the limiting distributions of the equilibration process by deriving Boltzmann H theorem from very benign assumptions. Once you know the distribution of the microstates, you can compute ensemble averaged values which you heuristically are convinced are equal to the time-averaged values (ergodic hypothesis). Digging deeper down this path is rarely done in a stat mech textbook because it is highly intricate. This is the subject of ergodic theory *.

Difficulty of kinetic theory ch.3 kardar:

Yes! it's very difficult :). I empathize. It has to be because you are literally deriving a fundamental result of statmech (boltzmann H) from microscopic laws of motion (hamiltonian flow). Kardar will walk you from F=ma (poisson bracket) -> BBKYG-> Boltzmann equation -> Boltzmann H in just a few pages, so strap yourself. You can of course skip that chapter and just assume entropy is maximized as a starting point and go straight to ch. 4, which is perfectly fine btw. However it seems you are not satisfied with a heuristic understanding of why things maximize entropy in the first place. If so, you got to do the hard work! No free lunch.

Note btw, that on the MIT ocw website, he posted all his lecture notes. If you notice he covers about 4-5 pages of his book in 1.5 hours of lecture: the book is dense.

A slightly more inspired derivation of Boltzmann equations is found in Landau vol. 10, section 1-5 (first 10 pages or so). Whether you like landau's or kardar better is a matter of taste.

The benefit of course is ch.3 is the gateway to other non-equilibrium studies (plasma physics, transport phenomena, hydrodynamics)

Math needed:

Regarding math prerequisites: the pre-requisite to study a grad stat mech textbook or anything in landau series is solid multi-variable calculus, differential equations and linear algebra. Depending on the type of engineering, there's significant overlap with the engineering curriculum. It seems you are already armed with a slew of those books.

Knowing the lagrangian & hamiltonian formulation of mechanics and some facilities with quantum is also assumed.

I just wanted to clarify "why" stat mech is taught in a certain way. There's a pretty coherent logic to it.

* Symmetry breaking is example of ergodicity breaking, but that's more advanced than kardar vol. 1 and you'll have to master that to appreciate the former. Most of the time, ergodicity "makes sense" just intuitively.

 

[vanhees71]

I'd say the foundations are pretty much clarified for about 80 years, i.e., since Pauli et al worked out the basic concepts of statistical physics for the quantum theory.

It's another question, how to introduce statistical physics in the most convincing didactical way. For me there are basically two convincing routes from quantum theory to quantum statistical physics. There's no really convincing route from classical mechanics to classical statistical physics, because you always have to borrow something from quantum theory (particularly the indistinguishability of particles). So it's anyway better to derive classical statistical physics as the corresponding limiting case of quantum statistical physics.

The two routes are:

(a) Information-theoretical approach to equilibrium statistical physics

Indeed there are good arguments to start with equilibrium statistical physics first, and then the information-theoretical approach is pretty convincing. It starts with working out the theory of the statistical operator as the general description of the quentum state, when it is impossible to determine the complete, pure state of a system or there is incomplete knowledge about the pure state. It's also necessary if you want to describe open quantum systems, which usually are not in pure states, even if they are part of a larger closed system that is in a pure state (reduced statistical operators of parts of a system that are entangled with other parts are usually not describing pure states).

If then the only knowledge about a system are the values of additive conserved quantities (or their averages) the Shannon-Jaynes principle of maximum entropy ("least prejudice") are the usual standard ensembles a la Gibbs (microcanonical, canonical, grand-canonical).

Another argument for the information-theoretical approach is that newer experimental investigations on the meaning of entropy in mesoscopic systems (like quantum dots), like the nice recent experiments on the "quantum Maxwell demons", clearly demonstrate the correctness of the information-theoretical interpretation of entropy. For more macroscopic situations that notion of entropy is in accordance with its notion in phenomenological thermodynamics.

(b) Kinetic-theory approach

Here you start from the general quantum dynamics of open quantum systems, usually on the example of the ideal gas (which has much broader ranges of applicability than first thought, thanks to Landau's fundamental concept of quasiparticles in many-body physics). There the statistical nature of many-body systems comes into the game because one cannot solve a practically "infinite tower" of equations for all the $n$-body distribution functions, containing the complete information of all the correlations within the system. So through coarse graining of some kind you through away "irrelevant information" on minute details which are unimportant for a description on more macroscopic scales, which leads to the H-theorem and thus to a "dynamical" justification for the maximum-entropy principle to characterize the equilibrium states, but of course the approach is much more general, also allowing to describe off-equilibrium phenomena and the derivation of the more macroscopic (semi-)classical theories to describe many-body systems like transport equations or hydrodynamics.

 

[ipsky]

Thank you for the explanation and clarification!

I always try to hear it from the horse's mouth when possible, which inadvertently means reading older books! Newer books on physics I have come across cost a fortune, weigh a ton, contain numerous printing errors, lack solutions to problems, and either lack rigour or suffer from rigour-mortis. That said, I have found excellent modern texts on biophysics that have included very good coverage of some aspects of statistical physics.

Since you come from an engineering background do you know about poisson brackets/hamiltonians/basic quantum?

I've a general idea, and I'm studying those topics alongside. My prior mathematics knowledge is limited to probability and information theory, linear algebra, single variable calculus, and Fourier analysis.

There's no really convincing route from classical mechanics to classical statistical physics, because you always have to borrow something from quantum theory (particularly the indistinguishability of particles)

This is one of the conceptual difficulties in the foundations of statistical physics, that I was referring to, which is not discussed in sufficient detail in modern textbooks in my opinion. An example is the study of Gibb's paradox, which should include a thorough comparison between Maxwell-Boltzmann, Bose-Einstein, Fermi-Dirac statistics and E. T. Jaynes comments. It is more of a discussion on what is commensurable and countable than just an exercise on calculating entropy.

(a) Information-theoretical approach to equilibrium statistical physics

This is what I'm following at the moment. And we had to investigate the quantum interpretation of entropy as part of the course, so quantum statistical mechanics was a natural continuation of the subject.