Physical appearance of maximum entropy

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Go easy, not an expert.

My intuition tells me that the maximum possible entropy in a given space is going to coincide with the arrangement requiring the most information to describe it. Let me know if this is wrong.

Ok, so now what I want to know is what an actual arrangement like this would look like physically if it could be realized. I want to know what it would look like if you blew it up so that the atoms were the size of marbles. Would it look random or would I see structure?

Are there an infinite number of such arrangements? Do max entropy arrangements have certain characteristics or certain physical structures that they will always have? Are they required to be similar structurally in some way? A purely random arrangement doesn't seem right because you could get some areas that happen to be easier to describe than they could have been. I am getting the impression that it will resemble a fractal, but that doesn't sit right because a fractal repeats parts of itself and that makes a description easier. It seems like it would require small yet complex structures that don't repeat and don't contain versions of themselves, nor are contained within larger version of themselves. No repeats or copies or translations would be allowed. It's almost like the opposite of a fractal intuitively. It constantly does not repeat. But what does that look like?

Anyone have any insight into this?

[edited] Also, it seems like you would have to repeat certain structures if your area was large enough because you'd run out of possibilities. Then what does it look like?
 
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  • #2
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There aren't infinitely many of such arrangements. Sure, there are a very large number of them, but it is finite, as QM says.

Every configuration is equally likely, so all the 2nd law says is that if you look at a system, you'll find it in such a way that from the outside it looks like one with highest entropy (since the probability is overwhelming). There is a difference between macroscopic properties and microscopic configuration, and you are confusing them.
 
  • #4
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Go easy, not an expert.

My intuition tells me that the maximum possible entropy in a given space is going to coincide with the arrangement requiring the most information to describe it. Let me know if this is wrong.
It goes just in the opposite, the more the entropy, less information needed to describe the system. That is why equilibrium systems are described by, typically, 2 or 3 variables.
 
  • #5
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The maximum amount of entropy that can be contained in a given volume would produce a black hole. In other words a black hole contains the maximum amount of entropy that can exist within the volume encompassed by the black hole.
Ok I read the links. That's pretty cool - it's coming together now. Ok so max entropy (or high enough entropy to form a black hole) would cause a black hole to form, which would immediately crush the arrangement of matter which caused it into a point with no entropy. But then that would violate the 2nd law, so that can't be what really happens. So the entropy can't be at the singularity and it can't be between event horizon and singularity because it's not stable there. So it must be on the event horizon. So anytime something falls in, the matter goes to the singularity, but the information describing the matter stays on the horizon, necessarily making the horizon larger in order to contain more information. So THAT's what Hawking was on about....

That brings up more questions though. So matter and the information describing it can be separate from each other? Or maybe they are the same thing so no need to be separate and nothing actually physically falls into the singularity?

What about the fact that you never see anything actually fall into a black hole because time slows for it and you see it stack up at the event horizon? That must be related.
 
  • #6
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What about the fact that you never see anything actually fall into a black hole because time slows for it and you see it stack up at the event horizon? That must be related.
That's an illusion. The matter does fall into the black hole it's only the light that you see that gets stuck at the event horizon.
 
  • #7
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Infalling matter takes fractions of a second to a few seconds to fall entirely into a black hole once it's passed the event horizon. As previously stated, the perception that it takes forever is merely an illusion.
 
  • #8
Watch "through the wormhole" with morgan freeman. There were two basic competing concepts. Hawking said there was a loss of information, but black holes emit hawking radiation every time they absorb mass. Susskind said there was no loss of information, and that our 3d universe is really projected from a 2d universe very far away. This came to be known as the holographic principle. I personally would rather say there is a loss of information becuase I dont see why you have to stick to classical boundaries when your talking about quantum mechanics.

http://en.m.wikipedia.org/wiki/Holographic_principle
 

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