# Gravitational Contraction and Entropy

In summary: I feel like I'm grasping at straws here, but maybe there's something I'm not thinking of.Thanks for trying to answer this question. I think it's a really interesting one and I'm sure there are experts on this subject out there! In summary, the entropy of the universe may or may not increase as a result of the gravitational contraction, but it's complicated and not well understood.
"Does the spontaneous contraction of a cloud of gas due to gravity violate the second law of thermodynamics? In other words, does entropy decrease as a result of the gravitational contraction?"

This question is posed in interesting article here:
http://www.mathpages.com/home/kmath573/kmath573.htm

If it was answered, it went right by me. In any case, it seems a conundrum.
Thanks

Sick question!

I would be inclined to say that the entropy of the gas decreases, and that's ok, a system's entropy can decrease, just as long as the big picture's entropy increases. So I would think about if the entropy of the universe increased even though part of it decreased... that might be a good place to start...

I would be inclined to say no. Take the case of a piston acting on a completely insulated gas cylinder. You can compress the gas, which is an adiabatic process (entropy = const.). I would argue that gravity is a similar mechanism, so entropy would be constant. Another way of looking at it, even though the volume is decreasing, the total kinetic energy is increasing (gravitational potential -> kinetic energy), so the number of accessible states does not actually decrease. If you include the case of the gas cloud radiating thermal energy, then entropy would not be const, just as an non-insulated piston would.

"Does the spontaneous contraction of a cloud of gas due to gravity violate the second law of thermodynamics? In other words, does entropy decrease as a result of the gravitational contraction?"

...

If it was answered, it went right by me. In any case, it seems a conundrum.
Thanks

It's only a conundrum because you are assuming that: entropy increase = spread out.
This is only the case when there is no force involved. With a force like gravity, the state where particles are spread out is actually a low-entropy state; the more they are concentrated together the higher the entropy becomes. Under the influence of gravity, there are many more microstates when the system has collapsed.
A black hole, for instance, being created out of a large amount of matter condensed into a very small area, has a huge entropy. There was a paper a while back where some guys claimed to have calculated the approximate entropy of the universe and the number turned out to be almost entirely due to black holes.

I'd say there are many instances where the second law is useless. If you look at the derivation of entropy, you'll find many assumptions that are only satisfied for kind of homogeneous systems which are completely randomized. Maybe an expert on ergodic theory can phrase this more mathematically correct.

The second law is no more than saying for flipping a coin the ratio between heads and tails tends to 1. But this doesn't have to be true if the coin is unfair or if the coin properties change with time. This second law is really only such a trivial probabilistic statement.

PS: Actually in this particular case you can probably regain the second law, but you have to redefine some sort of dynamic phase space. Therefore just being close together does not correspond to a low entropy. But maybe being in a special place or having a special velocity means low entropy.

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You have to be very careful about your intuition in this case. The heat capacity of a gravitationally bound system is negative. The first consequence is that every derived equation that assumes it's positive is wrong and you need to go back to first principles. The second consequence is that it cannot collapse unless it can lose energy to an external system. Therefore, it is not a closed system, full stop. The second law does not apply.

"It's only a conundrum because you are assuming that: entropy increase = spread out."

Yeah, it is dispersed in micro-states but not necessarily spread out in space as with background radiation.
I am distressed that such a fundamental concept is so difficult for me to get a firm handle on.

Thanks all.

Here's an interesting article on just this subject: http://math.ucr.edu/home/baez/entropy.html"

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You have to be very careful about your intuition in this case. The heat capacity of a gravitationally bound system is negative. The first consequence is that every derived equation that assumes it's positive is wrong and you need to go back to first principles. The second consequence is that it cannot collapse unless it can lose energy to an external system. Therefore, it is not a closed system, full stop. The second law does not apply.

Dear me, I am conumdrumed again. If the system is the universe as a whole (that is, no external sink), is it not true that there is a general trend toward increasing entropy?

jackiefrost said:
Here's an interesting article on just this subject: http://math.ucr.edu/home/baez/entropy.html"

Thanks, that is a great article.

He states that:

" * The energy of a gravitationally bound cloud of gas decreases as the cloud shrinks.
* The entropy of a gravitionally bound cloud of gas decreases as the cloud shrinks.
* A gravitationally bound cloud of gas has a negative specific heat. "

And playfully ends with:

"Well, I said I'd tell you the answer to this puzzle, but by now I've had a change of heart. I had so much fun figuring out the answer myself that I'd hate to deprive *you* of this pleasure. So go ahead, figure it out. But if you give up, click here for a hint. "

"So, you're wondering why gravity doesn't violate the 2nd law of thermodynamics, even though the entropy of a gas cloud decreases as it shrinks under its own gravitational pull? The answer is simple, but I'll just give you a hint. We've already seen that as it shrinks, it loses energy. The energy has to go somewhere. Where does it go? If you figure that out, you'll see that the total entropy is not actually decreasing - it's just leaving the gas cloud and going somehere else! "

Sorry to be so slow, but if you can touch a God-like finger of clarity to my forehead without burning too many Calories, kindly do so.

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## 1. What is gravitational contraction?

Gravitational contraction is the process by which a massive object, such as a star, shrinks in size due to the force of its own gravity.

## 2. How does gravitational contraction lead to an increase in entropy?

As a star contracts, it releases gravitational potential energy as heat, which increases the overall energy and disorder (entropy) of the system.

## 3. How does the second law of thermodynamics relate to gravitational contraction?

The second law of thermodynamics states that the total entropy of a closed system will always increase over time. Gravitational contraction is an example of this, as the increase in entropy from the release of heat cannot be reversed.

## 4. Can gravitational contraction occur indefinitely?

No, gravitational contraction is limited by the available supply of energy within the star. Once this energy is depleted, the contraction will stop and the star will reach a state of equilibrium.

## 5. What happens to a star as it undergoes gravitational contraction?

As a star contracts, its core becomes increasingly dense and hot, leading to nuclear fusion and the release of energy. The outer layers of the star may also expand and cool, leading to changes in the star's overall properties and characteristics.

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