Demystifying the second law of thermodynamics

Ask three thermodynamics engineers, get five answers. The generalization you're referring to is pretty accurate, but according to some interpretations it's just assumed to exist a priori and then we look for evidence of it.

But while it's unclear whether entropy is the result of some universal law or a hack we use to make the math work out, it definitely does make the math work out in closed systems of gasses.

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Entropy is a phenomenon of probability. This is a very incorrect way to put it but it gets closer to the intuition of definition:

   Disorder is more probable than order that's why things trend towards disorder. 

However it is only a probabilistic phenomena so technically low probability things can still occur. This is what the article is saying and he proves it with a bunch of math.

But the above is still technically incorrect because Entropy has nothing to do with disorder per say. Entropy is defined relative to a "system" and we can actually pick different systems where as entropy goes up while things become more organized and more ordered!

Keep in mind that a system is as much something that exists as well as properties of something we can arbitrarily define.

Say a system of loaded dice:

If my system consists of 100 weighted dice that flip up at 6 almost every time then entropy is increasing as I roll all the dice but the system is trending towards order: more sixes facing up.

Another system that trends towards order is the solar system. Gravity pulls particles to form ordered circular orbits and ordered spheres/planets because that is the way the system is configured. You have a bunch of random atoms but like the weighted dice, gravity pushes the system towards order and organization. But entropy is increasing!

Ever wonder why people say entropy always increases but you see weird ordered stuff in nature all the time like snow flakes and crystals? In those cases entropy is still increasing but producing order.

Basically in the systems I described above Ordered configurations are More probable then disordered configurations thus while "order" is increasing, entropy is also increasing. Once you understand this you'll have a better intuition of entropy and why it doesn't have to do with "disorder."

When people talk about stuff like entropy always goes up they say things like whenever you see something self organize then something else in the universe must become more disordered don't know what they're talking about. Yeah entropy trends towards higher values but this is not equivalent to disorder.

As for life on earth. Life on earth is a low probability phenomena. Something else is going on in this case but that's another discussion.

>has anyone formalized the idea that the second law can be interpreted as a general inability of computer programs to predict one another?

Arieh Ben Naim thinks entropy is better described by Shannon's Measure of Information. I haven't actually read any of his books, but I've been meaning to "one of these days".

http://ariehbennaim.com/books/index.html

The following papers make the argument that, at least for systems with a low initial entropy, "within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all."

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Quantum Solution to the Arrow-of-Time Dilemma

Lorenzo Maccone

Phys. Rev. Lett. 103, 080401 – Published 17 August 2009

The arrow-of-time dilemma states that the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e., entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.10...

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[Submitted on 30 Dec 2009]

A quantum solution to the arrow-of-time dilemma: reply

Lorenzo Maccone

I acknowledge a flaw in the paper "A quantum solution to the arrow of time dilemma": as pointed out by Jennings and Rudolph, (classical) mutual information is not an appropriate measure of information. This can be traced back to the quantum description underlying my analysis, where quantum mutual information is the appropriate measure of information. The core argument of my paper (summarized in its abstract) is not affected by this flaw. Nonetheless, I point out that such argument may not be adequate to account for all phenomena: it seems necessary to separately postulate a low entropy initial state.

https://arxiv.org/abs/0912.5394