Best way to self-study thermo/stat mech.

[X89codered89X]

I'm in grad school for systems/control engineering. I'm much more interested in the theoretical aspects of the subject as opposed to building physical systems. Maybe that makes me less employable, but regardless, a lot of my ideas now require the mathematics developed mainly in thermo/stat mech, but my EE undergrad degree doesn't really prepare me from the thermal physics/stat mech material very well, And I doubt I could be permitted to take a thermal physics undergraduate course even if for the sake of research. I have statistical mechanics textbooks, both of which appear to be written Well, but I do not seem to have the thermal physics prerequisite material. In addition, most of the "schaums teach yourself thermodyanamics" are more geared towards engineering, which means steam tables and physical systems, as opposed to the mathematical methods and content which is useful to me.

So the question is, how do I study thermal physics (and ultimately stat. mech) on my own? I'm very comfortable with self-study, but I'm also aware that without the right resources, it can be nearly impossible. I'm looking for recommendations on video lectures (if you know any that exist), practice problems with answers (so i can check my work), readable textbooks, etc. That go into the deep mathematics of the subject as opposed to preparing me for the trade.

Thanks for reading!

 

[Lavabug]

For thermo, the book by Callen is the most mathematically rigorous I've seen. About as pure theory as the subject gets. Very self-contained.

I like the book titled "Statistical Mechanics" by R. Kubo (not the 2-tome stat-physics series by the same author), it's not very verbose on the theory but is chock full of illustrative example problems and solutions to practically all the exercises. There are probably more theory-heavy books on SM, but it's worth checking and is definitely self-study friendly.

 

[Aero51]

Use Hills book. I have used it myself with great results!

From experience, read the book and summarize every few paragraphs in your own words in a separate notebook. Once you have finished the chapter take a break and solve 2-3 problems depending on the their difficulty.

https://www.amazon.com/dp/0486652424/?tag=pfamazon01-20

 

[X89codered89X]

Use Hills book. I have used it myself with great results!

From experience, read the book and summarize every few paragraphs in your own words in a separate notebook. Once you have finished the chapter take a break and solve 2-3 problems depending on the their difficulty.

https://www.amazon.com/dp/0486652424/?tag=pfamazon01-20

HA! I was referring to that stat. mech. book exactly, which appears to be written well and illustrates things clearly, but I think it will be better for me to go in depth with thermo first. For that I may use Lavabug's suggestion of Callen's book, which I've found online and looks good.

 

[Aero51]

Honestly the book goes through all the derivations from start you should be able to develop a physical intuition of the material.

 

[jasonRF]

What aspects of statistical physics are really what you eventually need to learn in order to help with your research?

 

[X89codered89X]

apologies to reigniting this thread but I finally have an answer for you JasonRF.

I'm studying stat. mech. in particular for the math methods involved. The usefulness of being able to make emergent predictions about an arbitrarily large collection of independent particles with their own states is an extremely powerful mathematical toolset. This tools in this toolset include are themselves their own fields: information theory, dynamical systems, stochastic calc, etc. etc. All of this will be useful.

Within this toolset, I see potential foundations to what could perhaps one day be strong AI, or at least a very popular field that is just "emergence science" in general.

 

[jasonRF]

In that case it seems like classical thermodynamics is not something you are really interested in, but just as a stepping stone to learnning the statistical physics. I don't know what the best book for you might be; I learned statistical physics essentially the same as you are - self-studying while I was an EE grad student (I used the book by Reif, which seemed self contained in terms of covering macroscopic thermo while emphasizing the statistical physics).

I do know of one book that may be interesting to you, although it does not emphasize math. Prof. Sethna at Cornell allows electronic download of his book from his site for free:
http://www.lassp.cornell.edu/sethna/
I think it is interesting and seems to be written from a viewpoint that applications outside of physics are important, although much of the material is actually in the problems.

jason

 

[kinkmode]

Stat mech and thermo were subjects I need to brush up on 'a bit' in grad school for my qualifier exams. It's probably not good advice, but I just read a crap load of books and worked old exam problems for a long time (with no solutions). To be fair, I did have a stat mech course in college.

The books I ended up working through were Reif, Callen, Huang, and Landau/Lifshitz. It was some time ago, so the details are blurry now. I had used Reif in undergrad, so I identify with that book the most. There's an incredible amount of information in that book, but it's dense, and my first time through in undergrad I missed or overlooked some important thoughts. Callen and Huang were two books I got based on recommendations from friends; I recall that they were more readable, but possibly not as thorough. Landau and Lifshitz is a great reference too, but not always accessible.

My reading and studying habits changed a lot that year. I finally learned to be much more meticulous in my studying and reading. I'd typically read a book/topic 2 times. The first a bit more quickly, highlighting sections, then a second time, making margin notes and summarizing topics in a notebook. In other words, working through material very thoroughly and slowly, while condensing the ideas contained within into my own words elsewhere.