Why Entropy isn't Mysterious
Audience: undergraduate
Tags: physicsinformation-theoryentropystatistical-physicsthermodynamics
My first ever animation, on an in depth explanation of what entropy is. It's a long format with some prerequisites (Lagrange multiplier technique, integrals, log properties). Any advice is welcome, I am well aware that the video has some problems. Entropy is often poorly understood, even among physicists. The goal of this video is to bridge de gap between information theory and statistical physics. It also tries to introduce Entropy very naturally by trying to solve a simple problem. At the end of this video you should be able to understand : * What information theory is * What entropy means in information theory * What the maximum entropy principle is * Why we need to use statistics to solve the dynamics of many particle systems * What entropy becomes in statistical physics * How to compute the microstates of a system in quantum and classical mechanics * Why the second law of thermodyanics is basically (almost) always true * What temperature really is, and why heat flows from high to low temperature
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Comments
The math is pretty clear, and the visuals are good. There’s a lot of information packed into this video, but that means there’s not enough space for all the necessary background (for instance, some of the quantum equations are presented without introduction). Each chapter could easily make for a full video on its own. Also, there are a few times when there are several equations on screen, and you refer to one of them. It would be helpful to highlight the relevant equation or variable.
This video is nice. I like the animation.
The video is too long for SoME, in my opinion. The organizers should filter the duration to less than 30’. But the most important thing is that it reminded me of many university lessons in which the important concepts were buried under lots of mathematical passages. The order of topics is also unclear: entropy in information theory was named after the physical quantity, so why present it first?
Well made video overall but I think you attempted to cover too much and I feel a bit lost as a result. The first chapter on entropy was very good - I especially liked the Lagrange multiplier part which I haven’t seen before.
After that, it gets a bit confusing. You define the classical Hamiltonian of postition and momentum which all seems fine and then immediately quantize it and start talking about 3 orthogonal harmonic osciallators spontaneously hopping around a lattice. You then keep alternating between classical and quantum descriptions for a while until you get to thermodynamics where you drop the quantum stuff altogether. From my position (not being a physicicst), I think you would have been much better to never introduce the quantum stuff as it seems like your end goal was with thermodynamics (linking stat mech and info) anyway. Or at least explain why it was relevant to your exposition.
Nevertheless, the video was well made - smooth animations and pretty good balance of intuition and formal details. Just needs a more focused narrative.
Neat overview of entropy. I am mostly familiar with this from the perspective of variational inference in machine learning (KL divergence, etc.) but it is cool to learn about the physics applications. Things started to go over my head from Chapter 2 onwards, so I can’t say much there.
This video was engaging in learning about how to best arrange entropy to achieve an efficient way of processing uncertainty. That being said, I think the video duration is a bit long, so an introduction for what the viewer would expect may aid in retaining viewers to watch through until the end of the video. I’ve set a Ranking score as an average of these individual scores, good luck: Motivation: 9 Clarity: 8 Novelty: 5 Memorability: 7
Successfully motivates why this is an interesting and important subject, but it seems it’s really hard to follow for broader audiences except for a very small slice with a very specific background
Lovely introduction to mathematical entropy and physics entropy. Very hard topic, which probably requires to be broken down in several videos. However, it is nice to have it in just one place for a review. The animations were great. The explanations were clear. The presentation was also clear. The video is quite educational.
Very informative video (no pun intended). Your explanations are great and easy to follow, your animations clean and simple, and your speed and tone felt natural. Not 100% happy about the quantum part, maybe simply call it a semi-classical part (a complete information theory treatment of quantum states requires a different approach (i.e. GPTs) since the postulates of Shannon IT are violated by QM). It would have been nice to mention but it’s a detail for sure. Overall, like many other videos I’ve seen here, I feel like your video would make a great lecture video. With lecture video I mean informative content made for someone that already wants to learn about your topic. To also be a great YouTube video that catches people who might normally have no contact with thermodynamics, I feel like it would need a bit more story, more examples, and interactive components like small riddles etc. Nonetheless, definitely above average content!