Thermodynamics and Statistical Mechanics
nicf.net
nicf.net
(You probably should know basic QM first, though)
https://www.amazon.com/Thermal-Physics-2nd-Charles-Kittel/dp...
For example the phenomenon of surface tension, which is usually taught as "surface energy" in a continuum way, but you can also view it "bottom-up" by looking at attractive forces between the individual particles. (Video by Eugene Khutoryansky, who has a large number of these sorts of animations):
https://www.youtube.com/watch?v=QKy6137F7OY "Surface tension as you've never seen it"
Similarly, statistical mechanics is the "bottom-up" view and thermodynamics is the "top-down" view.
EDIT: perhaps more relevant ones:
Molecular Temperature & Degrees of Freedom: https://www.youtube.com/watch?v=nqGtji3ZjoI
Brownian motion: https://www.youtube.com/watch?v=V7VtOa8pHno
I want to like these resources, but they seem to suffer from the common approach to teaching mathematics.
Namely, a complete disregard for a numerical approach, and sprinkling latex symbols throughout large blocks of text without a clear through line.
Reading education material like this feels like reading code from an llm. I am spending more time cross referencing and checking the statements than doing the thing I came to the material to work on.
> If we interpret the path integral in terms of the Wiener measure, then it does in fact solve our Wick-rotated Schrödinger equation.
I guess I’ll takes your word for it.
If you understand the material as well as your word count suggests than why omit numerical elucidation?
If you are unable to perform numerical analysis of these formulae than why should I trust your symbol mangling of them?
The audience that I had in mind for these pieces is mostly people who've had some amount of training in pure math; it came about because I felt (and still feel) like a lot of the existing resources for this stuff aren't presented in a way that lines up well with the way that people with that training often like to absorb information.
Speaking for myself, I don't think I would enjoy reading an article about the Feynman path integral that's full of tables and graphs with results of numerical experiments. My reaction to a piece like that would be "Okay, that's nice, but can you please just say what mathematical objects we're even talking about here first?" It sounds like you have the opposite set of expectations, which is totally fine, and that probably just means these aren't the articles for you, but there (I hope!) are also other people whose expectations are more in alignment with the presentation I went for. I don't think either of us is "wrong"; our preferences are just different.
“Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics.”
Goodstein also was the host of "The Mechanical Universe".
https://www.imdb.com/title/tt0396993/
I managed to snag one of the last copies before they went out of print.
My other favorite would be Brian Harvey's lectures although it never made the TV
https://www.youtube.com/playlist?list=PLhMnuBfGeCDNgVzLPxF9o... (this is about scheme, not statistical mechanics)
I had an experience in an interview for a Sr MLE role describing some previous work. Was unable to get through to the interviewer that the answer to the question of "which loss function did you use" can't always be found in a Medium listicle.
Hint: loss functions are negative log-likelihoods.
If the author ever lurks here, thank you so much for putting these online!