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> The thing I don't fully understand yet is heat entropy. Apparently when you take heat into account for everything, the disordered intuition suddenly becomes applicable. So if you have a system becoming more ordered with time, heat must be increasing somewhere to offset this increase in order. Maybe someone can explain this part to me?

You can extract work from order, and can create order with work. Consider this scenario:

We have two kinds of particles and two rooms. If we have one kind of particle per room it is pretty ordered, if we mix everything then it isn't ordered. Now, lets say we have two filters, filter 1 lets particle 1 through and filter 2 lets particle 2 through, but not the others. So we have a wall between the rooms made of these two filters. Particle 1 will just put pressure on filter 1 and vice versa. This way we can let particle 1 push their filter through room 2, which creates work, thus mixing particles a bit. Do the same with particle 2 and now we have mixed both and extracted the work from mixing the particles. We can reverse this process by moving the filters the opposite direction, dividing the particles again and this process will require work to perform.

Exactly how the filter work doesn't matter, as long as it lets through the other particles then the other particles will stabilize and eventually even out the pressure on the sides. It could be slow but it would work. Doesn't have to be perfect either, if probability isn't exactly the same for both particles you can do it over and over until you get the purity on each side you want. We already uses this to enrich uranium for example, so we can make filters for basically anything in theory.

Ok, but notice this argument is based on purely probabilistic assumptions and that all micro-states are equally probable to occur and do occur in time. There is still the question whether these assumptions are valid in a given physics system.

In physics we know much more about evolution of systems, for example in classical mechanics model of gas, there are deterministic equations of motion which also conserve some quantities like energy. So not all thinkable chaotic states are accessible, and the evolution of state is not a repeated random choice out of the whole set of states.

I envy you for your understanding of entropy. I understand a few simple aspects of it, but the deeper meaning eludes me. It does seem to be a useful concept which grants access to so many knowledge domains.

I understand one aspect of it in terms of probability. However another aspect of it eludes me as well, as I described in my last paragraph.

There's also a third angle from information theory. This type of understanding I haven't really studied in depth yet.

> Because chaotic configurations have a higher probability of occurring.

That seems like a non-explanation though. Why do chaotic configurations have a higher probability of occurring?

Because, as he said, there are more of them.

There are way way way more of them, so if you randomly select from the set of all possible configurations, you are much more likely to get something spread out and chaotic then something with a recognizable structure. As atoms and molecules bounce around, they are effectively randomizing. After a few dozen interactions each, they're basically in a new state. Repeat over and over and you're basically just drawing from that same set again. There's a chance that all of the air molecules could bounce to one side of the room at once, but the likely hood of that makes it something you won't see in the lifetime of the universe. So if you see a video where all the air rushes from half the room to fill the rest, you can be effectively certain you're watching the video forward and not in reverse.

From other replies to your question I understand that you use "chaotic" in the mathematical sense while other commenters use it in the colloquial ("random") sense.

I use it in the colloquial sense. Disordered, random.

12345 is less plentiful then 32415 or 32154 or .... What we considered "ordered" has less possibilities then "unordered" not just in a string of 5 numbers but for most systems. That should help you get the intuition. Lmk if you need more elaboration.

Master that entropy and you too can enjoy sending data over Internet without changing one bit of data: pulse-width modulation of inter-packet delay gaps.