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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

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- Thread starter BaghdadSerai
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- #1

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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

- #2

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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...

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- #4

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BaghdadSerai said:"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

- #5

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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.

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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- #7

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Yeah, it is

I am distressed that such a fundamental concept is so difficult for me to get a firm handle on.

Thanks all.

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

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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?

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

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,

The link being:

"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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