The Second Law of Thermodynamics

As another comment mentioned, this website does look like Time Cube at first sight.

However, the explanations of the second law of thermodynamics on the second page are quite decent and written in a humorous way. Of course it is not fully accurate because it does not use any math but I think it does a good enough job of explaining it to the lay person.

The explanations about human life at the third page are analogous at best. The situations that the author describes are similar to the workings of the second law but not a first principles outcome of it.

> Don't put me down. I could have snowed you with differential equations and diagrams instead of what you see everyday. We're being practical and visual rather than going the math route, essential as that is in chemistry.

> The big deal is that all types of energy spread out like the energy in that hot pan does (unless somehow they're hindered from doing so) They don't tend to stay concentrated in a small space.

I am trying to loosely connect big ideas here so I might be wrong. If there is fundamental feature of a universal law, then that feature must manifest itself at all scales, as the above statements tries to put forward visually. Maybe this idea of flow spreading out is very general and some kind of summarization of that finer grain flow to coarser flow in the form of Green's theorem or Stoke's Theorem is very general.

Kinematic Flow and the Emergence of Time

https://arxiv.org/abs/2312.05300

A neat little corollary to this is to look a little more closely at what temperature actually is. "Temperature" doesn't appear too often in the main explanation here, but it's all over the "student's explanation". So... what is it?

The most useful definition of temperature at the microscopic scale is probably this one: 1/T = dS / dU, which I've simplified because math notation is hard, and because we're not going to need the full baggage here. (The whole thing with the curly-d's and the proper conditions imposed is around if you want it.) Okay, so what does that mean? (Let's not even think about where I dug it up from.)

It's actually pretty simple: it says that the inverse of temperature is equal to the change in entropy over the change in energy. That means that temperature is measuring how much the entropy changes when we add or remove energy. And now we start to see why temperature is everywhere in these energy-entropy equations: it's the link between them! And we see why two things having the same temperature is so important: no entropy will change if energy flows. Or, in the language of the article, energy would not actually spread out any more if it would flow between objects at the same temperature. So there's no flow!

The whole 1/T bit, aside from being inconvenient to calculate with, also suggests a few opportunities to fuzz-test Nature. What happens at T=0, absolute zero? 1/T blows up, so dS/dU should blow up too. And indeed it does: at absolute zero, any amount of energy will cause a massive increase in entropy. So we're good. What about if T -> infinity, so 1/T -> zero? So any additional energy induces no more entropy? Well, that's real too: you see this in certain highly-constrained solid-state systems (probably among others), when certain bands fill. And you do indeed observe the weird behavior of "infinite temperature" when dS/dU is zero. Can you push further? Yes: dS/dU can go negative in those systems, making them "infinitely hot", so hot they overflow temperature itself and reach "negative temperature" (dS/dU < 0 implies absolute T < 0). Entropy actually decreases when you pump energy into these systems!

These sorts of systems usually involve population inversions (which might, correctly, make you think of lasers). For a 2-band system, the "absolute zero" state would have the lower band full and the upper band empty. Adding energy lifts some atoms to the upper band. When the upper and lower band are equally full, that's maximum entropy: infinite temperature. Add a little more energy and the upper band is now more full than the lower: this is the negative temperature regime. And, finally, when everything's in the upper band, that is the exact opposite of absolute zero: the system can absorb no more energy. Its temperature is maximum. What temperature is that? Well, if you look at how we got here and our governing equation, we started at 0, went through normal temperatures +T, reached +infinity, crossed over to -infinity, went through negative temperatures -T, and finally reached... -0. Minus absolute zero!

(Suck on that, IEEE-754 signed zero critics?)

And all that from our definition of temperature: how much entropy will we get by adding a little energy here?

Thermodynamics: it'll hurt your head even more than IEEE-754 debugging.

There is also an interesting relation between the second law of thermodynamics and the cosmological principle (which says "the distribution of matter is homogeneous and isotropic on large scales"):

The second law of thermodynamics says that the universe has an entropy gradient in the time dimension, while the cosmological principle says that the universe has no matter gradient in the spatial dimensions.

So together they describe how the universe (space-time) is structured, i.e. on the temporal dimension and the spatial dimensions.

It's also noteworthy that one enjoys the honorific "law" while the other is merely called a "principle". I wonder whether this is just an historical artifact or whether there is some theoretical justification for this distinction. (My intuition is that both are more "principles" [approximate tendencies?] than fundamental laws, since they don't say what's possible/impossible but rather what's statistically likely/unlikely.)

The classic Flanders and Swann explanation: https://www.youtube.com/watch?v=VnbiVw_1FNs

Excerpts: No one can consider themsleves educated who doesn't understand the basic language of science - Boyle's law: the greater the external pressure the greater the volume of hot air. I was someone shocked to learn my partner not only doesn't understand the 2nd law of thermodynamics, he doesn't even understand the first!

: Heat won't pass from the cooler to hotter! You can try it if you like but you'd far better notta!

M: Heat is work and work's a curse M: And all the heat in the universe M: Is gonna cool down, M: 'Cos it can't increase M: Then there'll be no more work M: And there'll be perfect peace D: Really? M: Yeah, that's entropy, Man.

I could never wrap my head around the abstract concepts used in these explanations because they don't connect to what is actually happening at the atomic level. As far as I could tell the actual particles are undergoing a constant process of reducing the potential energy induced by force fields between them, which means everything is just jiggling all the time and spreading further and further apart. Heat is just some metric describing the aggregate behavior.

2nd law only states a direction, however, does not determine the rate of change of things. It is also related to the spontaneity of reactions. What is the role of activation energy (or other weak/strong nuclear force potential barriers due to state).

What prevents everything happening all at once (just by obeying 2nd law is there a reason?). And if there is, is there a consistent formulation of 2nd law + other law that get this problem, at least macroscopically correct?

Repeal the Second Law! Free Energy for Everyone!

Is anyone else hearing the word thermodynamics pronounced by Homer J?

It's tinting my ability to read this.

Related: https://www.sidis.net/animate.pdf