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I'm trying to properly understand the meaning of entropy, and how the universe is moving from an orderly state to a chaotic one.

If a glass of wine (for example) only has meaning to a human, what makes a shattered spilled glass any less orderly than a full whole glass?

Or if a particle is observed, and it's probability wave collapses, isn't this moving from a 'chaotic' (uncertain and in many places), to an 'orderly' (certain, definite position) state?

Also, isn't the formation of stars, planets, galaxies etc... a move from a more chaotic state to a more orderly one?

Just trying to get some perspective into what the true meaning of entropy is and why it's important.

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Haven't got time to prepare a proper answer at the moment, but you may be interested in this paper which answers many of your questions. A key point is gravitational entropy contribution increases when stuff clumps together gravitationally, and the ultimate form of this is the black hole. –  twistor59 Dec 13 '11 at 8:37
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If a glass of wine (for example) only has meaning to a human, what makes a shattered spilled glass any less orderly than a full whole glass?

Symmetries. Symmetrical systems have smaller entropy as defined by delta(S)=delta(Q)/T) because to break the symmetry energy/heat has to be expended.

Or if a particle is observed, and it's probability wave collapses, isn't this moving from a 'chaotic' (uncertain and in many places), to an 'orderly' (certain, definite position) state?

The crux in this sentence is "observed". To observe there must be interactions and the interactions of observing add energy and disorder to the system. It is only in closed hermetically systems that the entropy is 0 or increasing statement can be evaluated. Think of biological systems. They are par excellence reducing entropy in their bodies, but they are not in a closed system, they die if the y cannot continually exchange energy and chemicals with the larger surroundings increasing entropy in the exchanges.

Also, isn't the formation of stars, planets, galaxies etc... a move from a more chaotic state to a more orderly one?

In an individual star, no, the heat goes up within when the star is formed from the big bang debris, much faster than the temperature which starts at near zero Kelvin; also a lot of radiation is created and escapes, increasing the entropy of the universe.

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Thanks! It seems my basic understanding of entropy was (as I expected) a little wonky, so I'm glad you were able to give me explanations for each of my examples and clarify the why. –  machinemessiah Dec 13 '11 at 15:58
    
What does "the heat goes up" mean? Entropy is the line integral over a reversible path of the heat that enters the system divided by the temperature. Just from your statement I don't see why this must be positive. I would've guessed that the entropy of a star/planet during formation went down, not up, and that this was compensated with an increase in the rest of the universe. –  Arnoques Dec 13 '11 at 16:50
    
@Arnoques If we go to the statistical mechanics definition of entropy in en.wikipedia.org/wiki/Entropy , matter that is close to 0 kelvin when coalescing gravitationally increases its available phase space since the average kinetic energy increases and therefore the number of possible microstates increases. There is also a relevant comment by twistor59 above. –  anna v Dec 13 '11 at 20:27
    
Ok, it's clearer now. Thanks! –  Arnoques Dec 13 '11 at 20:42
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