4 ms·

Thermodynamics and Statistical Mechanics

77 points by Anon84 3y ago

keepamovin 3y ago
I really enjoyed my chemical kinetics, statistical mechanics and thermodynamics classes in undergrad chem. Learning that temperature as measured was an emergent property, and that entropy increases with higher temperature due to the larger number of microstates / ensembles, was pretty fucking kewl! :) ;p haha
HPsquared 3y ago
The way large numbers of particles come together and start to behave like a continuum, is quite well represented by looking at simulations of a bunch of spheres with forces applied. 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 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 https://www.youtube.com/watch?v=nqGtji3ZjoI Brownian motion: https://www.youtube.com/watch?v=V7VtOa8pHno https://www.youtube.com/watch?v=V7VtOa8pHno
- 3abiton 3y ago
  Do you know any decent framework (ideally using python) to visualize such interactions?
bjornsing 3y ago
I have to take this opportunity to recite the opening passage of the introduction to thermodynamics and statistical mechanics in David L. Goodstein’s «States of Matter» from 1985: “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.” From https://x.com/rainmaker1973/status/1724781799308456152 https://x.com/rainmaker1973/status/1724781799308456152
- bryanrasmussen 3y ago
  Evidently still alive - what a fighter!
- godelski 3y ago
  Can I introduce you to BBC's Dangerous Knowledge? It covers Cantor, Boltzmann, Gödel, and Turing. Part 1: https://www.dailymotion.com/video/x8c24qz https://www.dailymotion.com/video/x8c24qz Part 2: https://www.dailymotion.com/video/x8c24r0 https://www.dailymotion.com/video/x8c24r0
- WalterBright 3y ago
  Prof Goodstein was my freshman physics professor. I didn't realize at the time how lucky I was. Goodstein also was the host of "The Mechanical Universe". https://www.imdb.com/title/tt0396993/ https://www.imdb.com/title/tt0396993/ I managed to snag one of the last copies before they went out of print.
  - kwoff 3y ago
    I loved that series. It's on Caltech's youtube channel: https://www.youtube.com/playlist?list=PL8_xPU5epJddRABXqJ5h5G0dk-XGtA5cZ https://www.youtube.com/playlist?list=PL8_xPU5epJddRABXqJ5h5...
  - srean 3y ago
    "The Mechanical Universe" ... now you are talking about peak of pedagogical achievement that TV ever scaled. My other favorite would be Brian Harvey's lectures although it never made the TV https://www.youtube.com/playlist?list=PLhMnuBfGeCDNgVzLPxF9o5UNKG1b-LFY9 https://www.youtube.com/playlist?list=PLhMnuBfGeCDNgVzLPxF9o... (this is about scheme, not statistical mechanics)
- dcuthbertson 3y ago
  What an attention grabber! If only more textbooks introduced their topics so as to capture the imagination and set the reader on a path of possible danger and intrigue.
roenxi 3y ago
I'd second the recommendation of An Introduction to Thermal Physics by Daniel V. Schroeder if anyone is looking for an undergrad level text. It is on my shortlist of "best undergrad textbooks read". It is also physically quite a small book; the quantum physicists must have some insight into density.
- BeetleB 3y ago
  I know many hated it, but thermodynamics never clicked for me until I read the book by Kittel/Kroemer. (You probably should know basic QM first, though) https://www.amazon.com/Thermal-Physics-2nd-Charles-Kittel/dp/0716710889 https://www.amazon.com/Thermal-Physics-2nd-Charles-Kittel/dp...
chombier 3y ago
Off-topic, but this whole website is a gold mine. I just finished reading "Coordinate-Free Linear Algebra" and "Hamiltonian and Lagrangian Mechanics", making tensor products, Lie derivatives and Poisson brackets finally click. Thermodynamics is next on my list. If the author ever lurks here, thank you so much for putting these online!
- nicf 3y ago
  I do! Thanks for the kind words. I'm happy to hear someone enjoyed the linear algebra article --- after I finished that one and heard from some people who tried to read it I ended up with the impression that I'd pitched it too hard, so it's nice to know someone got something out of it.
- deleted 3y ago
  [deleted]
nicf 3y ago
Hi, this is the author. It's been really fun to see these articles getting a little more attention. I wanted to repeat something I said when my website was posted here a couple of weeks ago, which is that I'm a private math tutor. I've been filling up a lot more than usual lately thanks to HN, but I do still have a little space! More info here: https://nicf.net/tutoring/ https://nicf.net/tutoring/
- super_mario 3y ago
  As fellow mathematician tutoring my son I found all of the articles incredibly useful. Thank you for writing them and making them freely accessible. Awesome work.
  - nicf 3y ago
    That's very lovely to hear! Thanks for sharing that.
- iburrew 3y ago
  Some constructive feedback: 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?
  - wholinator2 3y ago
    Standard results omitting tedious derivations is a standard practice in all educational material of upper level physics. "Derivation left to reader", etc. I personally greatly enjoy the fact that i get to decide how much detail i want. I can get the gist, a moderate exploration, or a deep dive if i have the time. Keep in mind, this person did not have to make this resource, and if you don't like it you don't have to read it. I greatly appreciate a breadth of resources when learning a topic and this is an amazing addition to my learning resources. If you absolutelyneed every single detail of every single assertion then look it up, but i can never expect a human doing this in their free time as a free gift to write dozens of textbooks about every facet of physics. Keeping every single detail in would make these prohibitively time consuming to create in a way that i don't think a free resource could support
uoaei 3y ago
The parallels between statistical mechanics and machine learning are eerily profound. Optimization theory describes systems and their evolution toward lowest-energy states, the landscape that optimization traverses and the dynamics by which it does so are described by statistical mechanical principles. 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.

77 points by Anon84 3y ago

I really enjoyed my chemical kinetics, statistical mechanics and thermodynamics classes in undergrad chem. Learning that temperature as measured was an emergent property, and that entropy increases with higher temperature due to the larger number of microstates / ensembles, was pretty fucking kewl! :) ;p haha

HPsquared 3y ago

The way large numbers of particles come together and start to behave like a continuum, is quite well represented by looking at simulations of a bunch of spheres with forces applied. 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 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 https://www.youtube.com/watch?v=nqGtji3ZjoI Brownian motion: https://www.youtube.com/watch?v=V7VtOa8pHno https://www.youtube.com/watch?v=V7VtOa8pHno

3abiton 3y ago
Do you know any decent framework (ideally using python) to visualize such interactions?

bjornsing 3y ago

I have to take this opportunity to recite the opening passage of the introduction to thermodynamics and statistical mechanics in David L. Goodstein’s «States of Matter» from 1985: “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.” From https://x.com/rainmaker1973/status/1724781799308456152 https://x.com/rainmaker1973/status/1724781799308456152

bryanrasmussen 3y ago
Evidently still alive - what a fighter!
godelski 3y ago
Can I introduce you to BBC's Dangerous Knowledge? It covers Cantor, Boltzmann, Gödel, and Turing. Part 1: https://www.dailymotion.com/video/x8c24qz https://www.dailymotion.com/video/x8c24qz Part 2: https://www.dailymotion.com/video/x8c24r0 https://www.dailymotion.com/video/x8c24r0
WalterBright 3y ago
Prof Goodstein was my freshman physics professor. I didn't realize at the time how lucky I was. Goodstein also was the host of "The Mechanical Universe". https://www.imdb.com/title/tt0396993/ https://www.imdb.com/title/tt0396993/ I managed to snag one of the last copies before they went out of print.
- kwoff 3y ago
  I loved that series. It's on Caltech's youtube channel: https://www.youtube.com/playlist?list=PL8_xPU5epJddRABXqJ5h5G0dk-XGtA5cZ https://www.youtube.com/playlist?list=PL8_xPU5epJddRABXqJ5h5...
- srean 3y ago
  "The Mechanical Universe" ... now you are talking about peak of pedagogical achievement that TV ever scaled. My other favorite would be Brian Harvey's lectures although it never made the TV https://www.youtube.com/playlist?list=PLhMnuBfGeCDNgVzLPxF9o5UNKG1b-LFY9 https://www.youtube.com/playlist?list=PLhMnuBfGeCDNgVzLPxF9o... (this is about scheme, not statistical mechanics)
dcuthbertson 3y ago
What an attention grabber! If only more textbooks introduced their topics so as to capture the imagination and set the reader on a path of possible danger and intrigue.

roenxi 3y ago

I'd second the recommendation of An Introduction to Thermal Physics by Daniel V. Schroeder if anyone is looking for an undergrad level text. It is on my shortlist of "best undergrad textbooks read". It is also physically quite a small book; the quantum physicists must have some insight into density.

BeetleB 3y ago
I know many hated it, but thermodynamics never clicked for me until I read the book by Kittel/Kroemer. (You probably should know basic QM first, though) https://www.amazon.com/Thermal-Physics-2nd-Charles-Kittel/dp/0716710889 https://www.amazon.com/Thermal-Physics-2nd-Charles-Kittel/dp...

chombier 3y ago

Off-topic, but this whole website is a gold mine. I just finished reading "Coordinate-Free Linear Algebra" and "Hamiltonian and Lagrangian Mechanics", making tensor products, Lie derivatives and Poisson brackets finally click. Thermodynamics is next on my list. If the author ever lurks here, thank you so much for putting these online!

nicf 3y ago
I do! Thanks for the kind words. I'm happy to hear someone enjoyed the linear algebra article --- after I finished that one and heard from some people who tried to read it I ended up with the impression that I'd pitched it too hard, so it's nice to know someone got something out of it.
deleted 3y ago
[deleted]

nicf 3y ago

Hi, this is the author. It's been really fun to see these articles getting a little more attention. I wanted to repeat something I said when my website was posted here a couple of weeks ago, which is that I'm a private math tutor. I've been filling up a lot more than usual lately thanks to HN, but I do still have a little space! More info here: https://nicf.net/tutoring/ https://nicf.net/tutoring/

super_mario 3y ago
As fellow mathematician tutoring my son I found all of the articles incredibly useful. Thank you for writing them and making them freely accessible. Awesome work.
- nicf 3y ago
  That's very lovely to hear! Thanks for sharing that.
iburrew 3y ago
Some constructive feedback: 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?
- wholinator2 3y ago
  Standard results omitting tedious derivations is a standard practice in all educational material of upper level physics. "Derivation left to reader", etc. I personally greatly enjoy the fact that i get to decide how much detail i want. I can get the gist, a moderate exploration, or a deep dive if i have the time. Keep in mind, this person did not have to make this resource, and if you don't like it you don't have to read it. I greatly appreciate a breadth of resources when learning a topic and this is an amazing addition to my learning resources. If you absolutelyneed every single detail of every single assertion then look it up, but i can never expect a human doing this in their free time as a free gift to write dozens of textbooks about every facet of physics. Keeping every single detail in would make these prohibitively time consuming to create in a way that i don't think a free resource could support

uoaei 3y ago

The parallels between statistical mechanics and machine learning are eerily profound. Optimization theory describes systems and their evolution toward lowest-energy states, the landscape that optimization traverses and the dynamics by which it does so are described by statistical mechanical principles. 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.