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I've been searching around and haven't found a satisfying answer to this. A lot of sources just give examples of supposedly reversible processes (such as pool balls hitting each other) actually losing very small amounts of heat to friction, drag, or some other usually ignored facet of the system.

Looking for more rigorous definitions to try and figure it out, I went to Wikipedia. But this only made everything seem circularly defined: reversibility is defined with the condition of no change in entropy, which is a state defined using the Carnot Cycle, which assumes reversibility. I assume this is merely a fault of Wikipedia's nature; the articles can't all coordinate and avoid circularity.

Thinking about it on my own, I couldn't reason why a possible (yet astronomically improbable) process cannot be truly reversible. For instance, take just two identical particles in a vacuum with equal initial velocities away from each other. Of course, this will likely never happen, but it's at least theoretically possible. Gravity should pull them back to their initial positions. Where is the energy transfered or converted here?


In essence, what exactly is reversibility, and how do we know it can't happen in a finite time?

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The long story short is "we don't know." We actually don't know any laws of physics, if you get down to it. None of them. The universe is what it is, and it behaves the way it behaves. That's really all we can say for sure.

Now we can say that we have found laws which we have no evidence to suggest they're ever broken. We have laws that we have put to some pretty stringent tests, like making miniature suns on Earth and testing the laws deep in their nuclear fires. But there's no way science can be absolutely certain.

(This, by the way, is a pet peeve of mine. Science is taught to students as though it has the capability to state exactly how the world works, when it's really just (one of) the best approach(s) we've found so far for modeling how the world works)

That being said, what we can do is look at thermodynamics and say what the universe would need to be like in order to have a truly reversible process. One hypothetical case where this could occur is in a perfectly anti-symmetric universe that started from nothing and will end with nothing. Everything we see in such a universe comes in pairs which eventually annihilate.

It's trivial to show that this is a reversible process. You started with zero, and you end with zero. We might even see interesting processes within this which appear to be non-reversible, but in reality it's just an illusion which vanishes when the two halves of that universe annihilate. This would account for the apparent non-reversibility we see.

In practice, we have no evidence to suggest the universe is like the universe I just described. You could model it that way, a parallel universe which will cause everything we do to simply vanish, but you could also model it as a non-reversible universe and the predictions will be identical all the way up to that magical end of days where the parallel universes collide, or not.

I like to think about this sort of thing pedantically, so I have to point out that the answer is "we don't know." However, practically speaking, we have done an enormous amount of study on thermodynamic systems, and all of the evidence we've collected fits so well with "everything is non-reversible" that it is reasonable to just assume this is true, and work from there. Only when you get into the really deep philosophical and mathematical rabbit holes do you need to consider a more nuanced position.

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  • $\begingroup$ So, in short, science proceeds on evidence of absence, yet is inherently mute on absence of evidence? $\endgroup$ – Glenn Slayden Dec 1 '17 at 1:47
  • $\begingroup$ Great answer, especially tying it in with the bigger view. Resolved all of my confusions except one smaller one: any idea whether my example in specific is reversible or not, and why? $\endgroup$ – Vedvart1 Dec 1 '17 at 1:57
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    $\begingroup$ @Vedvart1 No, it's not reversible, but that's not immediately evident until general relativity. The particles accelerating back to their initial position will emit gravity waves, which release energy out of the system. I think you could actually construct a theoretical perpetual motion machine, if you played your cards very carefully to avoid known loss sources, but if there exists a universe outside of the system (which there always will be), it'll muck with your ability to get it perfect. $\endgroup$ – Cort Ammon Dec 1 '17 at 3:55
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    $\begingroup$ Another topic which may interest you is metastability, which is what we see if we have a ball resting right on the top of a hill. If the ball were to be a little to the left, or a little to the right, it may fall to that side, but there's a perfect balancing point on the top. In theory there is a point at the top where the system has energy (not in the ground state), but entropy never increases -- it just stays there. In practice, tiny effects will perturb the balance and cause the ball to fall. $\endgroup$ – Cort Ammon Dec 1 '17 at 3:57
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    $\begingroup$ Things like the gravitational pull of Jupiter start to matter in those exotic impossibly precise balances. I'm always amused by that because I'm sure the astrologers would love it when they realize that, in this particular experiment, whether Jupiter is ascending actually affects the future! $\endgroup$ – Cort Ammon Dec 1 '17 at 3:58

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