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Old   February 27, 2021, 09:09
Default Statistical mechanics references
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Hello everyone,

can you suggest a modern (i.e., up to date in both coverage and formalism), textbook like (i.e., complete but for dummies), reference on statistical mechanics that, starting from the Hamiltonian mechanics approach works its way down to the Liouville equations, the BBGKY hierarchy, and eventually any other approximation, like the Boltzmann equation and the Chapman-Enskog theory, that allows, in the end, to obtain the Navier-stokes equations, possibly for both gases and liquids?

In the years, I never really needed any formal approach to this, and I was fine with the book by Gombosi (Gaskinetic Theory) and what I could get from fluid mechanics (e.g., Batchelor) or thermodynamics (e.g., Callen) books, but never really had the stomach to go trough the Chapman-Cowling book or the Landau volumes 5 and 10 (to my great disappointment, considering that I bought them both).

I guess I'm after a book on the same complexity level as the Gombosi one, but probably wider in scope and perspective, if it exists at all. Of course, any lecture note or similar material would work as well.

Do you have any suggestion?

Thanks
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Old   February 27, 2021, 09:33
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Paolo:

I don't know about "recent;" it's been many moons since I studied statistical mechanics. Personally I don't know how much stat mech is covered by the Gombosi book, but judging from superficial viewing of the chapters I guess it is more a gas dynamics book than a stat mech book (as its title suggests).

If you are looking for a reasonably painless theoretical foundation (i.e., it explains well without sacrificing formalism) I would recommend "Physical Chemistry" by Peter Atkins. This might be a undergrad level text book for physics or chemistry majors, but the theoretical treatment on the subject in question is in my opinion far superior than most graduate texts aimed at mechanical engineers.

Ashley Carter also wrote another book on statistical thermodynamics (look up the title as I forgot). I didn't like it too much as I found that he took too much effort in making the math "easier", to the point key steps were skipped in derivations and proofs. Those with very solid math background will probably stomach the leaps of faith, but it is still very annoying. Maybe we engineers got a reputation of being bad in math.

It's been a while since I touched Cullen. If memory serves the whole part on stat mech is so sketchy, as if it doesn't belong in the first place.

Gerry.

P.S. - As far as I know, the furthest most stat mech textbooks go in fluid dynamics are definitions of pressure and viscosity. I have not seen any derivation of the NS equations from that approach. Using the lattice-Boltzmann equation, yes, but not from something so low level.
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Last edited by Gerry Kan; February 27, 2021 at 11:48.
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Old   February 27, 2021, 09:55
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Thanks Gerry, I will explore both.

Actually, the Atkins book seems something that, even if it doesn't turn out to be what I exactly wanted (probably too wide in scope), might be worth reading nonetheless.
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Old   February 27, 2021, 11:51
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Paolo:

Atkins is a very useful book. When I started my PhD (many moons ago) the 4th edition was out. I ended up buying the 2nd edition used, and it is as useful now as it was then. I never truly understood classical and statistical thermodynamics until I read it.

Gerry.
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Old   February 27, 2021, 12:55
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Paolo, you don't like the classic Statistical Physics bu Landau? Not recent but ...
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Old   February 28, 2021, 09:12
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Well, I haven't open the Landau books in more than 10 years, but I remember being able to appreciate them only for those topics in which I was already educated, and even in that case I completely missed the pedagogical aspect.

Now, I plan to read this material in bed, 1 or 2 hours per night. And I know that this is impossible to do proficiently when I am not already acquainted with the mathematical notation. Tried with the Chapman book just as a test, and I failed spectacularly, because at that time of the day, especially if it is just for amusement, I am unable to process anything beyond what I have under the eyes in that very moment.

So, I have very littlr faith in being able to achieve anything with Landau

EDIT: nonetheless, I can probably give it a try while I keep searching
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Old   February 28, 2021, 10:33
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Just to mention, I just found this book:

Klimontovich: Statistical Theory of Open Systems

which seems to exactly follow the path I was looking for without being too scary in notation. I'll probably add it to the one by Atkins and let you know if it turns out well or I inevitably fall asleep each time I try to read it.
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Old   March 1, 2021, 02:49
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My (limited) experience with Russian works is that their mathematical treatment as so dense that it is frightening and amazing to read. Gerry.
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Old   March 1, 2021, 02:57
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My favourite is

McQuarrie, Statistical Mechanics

It covers the topics you listed.
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Old   March 1, 2021, 03:53
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Quote:
Originally Posted by praveen View Post
My favourite is

McQuarrie, Statistical Mechanics

It covers the topics you listed.
Indeed seems like a great reference. So, considering that now I'm scared of the Russian math, here it is the plan. I'll go trough the following order:

1) McQuarrie
2) Klimontovich
3) Atkins

If I will ever be able to finish these 3 I'll probably give a(nother) shot to Landau as well. Hopefully then, even if just by osmosis, some knowledge should eventually flow into my head.
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