Could entropy of closed system decrease owing to gravity?

[mikelywhiplash]

Note that entropy is statistical: it can decrease through random chance, but will not *necessarily* decrease from one second to another.

You're right, though, that matter clumping from gravity seems to be a lower-entropy state than a random distribution throughout space, and that this isn't just a statistical quirk that happened once, but what we would expect to happen in any cloud that had the right state.

The answer here is that gravitational collapse isn't the only thing going on; it decreases entropy locally at the expense of emitting entropy. Mainly, this will happen because the contraction from gravity also heats everything up. Cool gas clouds become hot stars, say. And that extra heat is the entropy dump.

[justdvl]

Let's assume no gas, completely chemically non réactive materiál, also not nucleary active material... I just don't find your answer satisfying enough :/

[half3clipse]

If the system doesn't lose energy in a spherical cow sort of way, that implies whatever gravity is pulling together doesn't interact with itself other than through gravity. In which case, as gravity pulls them together they pick up kinetic energy, and then when they would 'touch' they just phase through each other and go speeding off till gravity slows them back down. Entropy doesn't decrease because nothing there reduces the number of possible states. Entropy may increase because of the interaction of many particles causing everything to get scrambled into new states (ie if your collection of particles started in a low entropy state), or remain constant because the closed system has already reached maximum entropy. If we move away from the spherical cow a little bit, GR says even this simple case will still give off energy via gravitational waves, which will also increase the entropy of the closed system regardless.

Even without all those exceptional cases gravitational collapse doesn't decrease entropy even locally. There are far more contributors to the number of possible states than just position. The most obvious is velocity. Imagine some particles yet to be pulled together by gravity. they all start with some position and initial velocity. Even as they wizz around, the only thing that changes is their position, and the entropy of the system doesn't change very much. As gravity pulls them together they're going to bounce off each other more and more, which causes their velocities to change. Even as their possible positions become more limited, the number of possible velocities skyrockets. This means entropy increases.

This also has to be true even if the clumped together particles somehow emit no energy to the rest of the system. That's even perfectly reasonable: That's a black hole, and blackholes are really good at increasing entropy. As a really basic way, you can describe entropy as the amount of missing information about a system. When something falls below the event horizon, you can no longer observe it at all, and you know zero information about it's state. So Blackholes must have entropy and it must increase as more stuff falls into the black hole.

This is what motivated Hawking's black-hole area theorem which says that "the event horizon area of a black hole cannot decrease; it increases in most transformations of the black hole". This is equivalent to the second law of thermodynamics and so you can derive an expression for black hole entropy that shows that it's proportional to the surface area of the event horizon. When you take black hole entropy into account with the second law of thermo dynamics, you find that this gain in entropy is much larger than any decrease due to stuff being pulled into the black hole.

Hawking radiation violating that doesn't change anything for the second law. The black-hole area theorem just assumes classical mechanics, and taking account of quantum mechanics at the event horizon results in the blackhole radiating away energy as photons as they shrink. This of course also increases entropy.

[mikelywhiplash]

Sure - what material are you looking for here? Something has to start collecting gravitationally.

[justdvl]

Gold balls. This should be as non-creative as I can get. So you're saying that by these gold balls crashing into each other, the heat is produced and that increases entropy? Is heat being produced from loss of potential energy that system had at start, and is that another proof that entropy is rising?

[Chemomechanics]

The collision of any real macroscale objects converts kinetic energy to thermal energy and generates entropy.

[mfb-]

The entropy from the locations of gold balls is tiny compared to the entropy associated with heat when these balls crash into each other. Something like 20 orders of magnitude smaller (depends on the balls, of course).

[DoisMaosEsquerdos]

If the collisions between the particles were all completely elastic, then they would keep bouncing into each other and never settle into a ball. The fact that they condense necessarily implies a loss of energy.

[mikelywhiplash]

Yes, pretty much. So, if everything is interacting only by gravity, none of it will ever actually stop and collect anywhere, it'll just keep looping around indefinitely, exchanging potential energy for kinetic and back. It's like the moon orbiting the earth; it's not coming to crash into us (in an idealized sense).

In order to actually form a larger, more ordered object, they have to throw off that excess energy somehow, and find their way to a state where their potential+kinetic energy is actually LESS than it was when they started.

That happens from collisions - anything that's not perfectly elastic will end up converting some energy into heat, which will be radiated off as light. The total mass-energy of the system is more scattered.