What if the Second Law could be violated?

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BlackSails
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Re: What if the Second Law could be violated?

Postby BlackSails » Mon Apr 27, 2009 2:08 pm UTC

Forum Viking wrote:
frezik wrote:The second law is a strange exception to the usual laws, in that it's based on probability rather than absolutes. For instance, it is theoretically possible for all the oxygen molocules in the room to organize themselves into one little corner. Such a room would have "broken" the second law by being more organized, but it's so unlikely to happen that we discount it entirely.

I suspect that a universe where the second law could be violated would have some frelled up laws of probability to go with it.
Infinite limits! Yay! Entropy's a weird, and cool thing. It almost seems that if we had a big computer to keep track of everything, then there would be no entropy. I think the refutation is that the computer would have to keep track of itself, and this is for some reason impossible.


You can also refute it with QM. In QM, not only is the future position and momentum of a particle indeterminate but the past trajectory is as well

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Re: What if the Second Law could be violated?

Postby airplanespaceship3 » Mon Apr 27, 2009 9:57 pm UTC

BlackSails wrote:Non-conservation of energy is a fundamental problem. It is the cornerstone upon which all of science rests. You could not overturn this principle without simultaneously overturning all of modern science.


Isn't Conservation of Energy the 1st Law? I agree violating *that* would result in significant upheaval. I would, however, think violating the 2nd Law would not be nearly as catasrophic. The same way we learn Newtonian mechanics even though relativity is more accurate, today's thermodynamics would still be mostly applicable in a post-2nd Law world; since 2nd Law violators are not readily observed, the 2nd Law would still be a useful tool in describing just about every process except those hypothetical violators.
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Re: What if the Second Law could be violated?

Postby Yakk » Tue Apr 28, 2009 12:13 am UTC

A possible fear would be a sum over paths based model of QM 'finding' such a possibility, and positive entropy changes leaking into the physics where it isn't supposed to get.

...

The thing is, entropy increase can also be described as information increase. It takes more bits of information to describe a room in which all of the particles of air are spread out, than one in which all of the particles are in a corner. In some sense, it takes more information to describe a high-entropy universe than a low-entropy universe.

From that perspective, the fact that we can remember the past and not the future makes sense. Remembering the past is easy, because in the present there is more information hanging around than the past.

Imagine you had a bunch of inelastic strings and a large funnel. If the top of the funnel is filled with strings, you cannot make the strings get out the bottom of the funnel. But if the bottom of the funnel is full of strings, you have plenty of room at the top to have all of the strings. Memory (the strings) can go from low entropy (small end of funnel) to high entropy (large end of funnel), but not backwards, because there isn't enough room.

You'd think "but you can get most of it" -- except in our universe, the funnel of entropy is very very steep. We measure entropy using exponential units for a reason. Every 'unit' of entropy that you generate is an exponential increase in the amount of information required to describe the system.
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Re: What if the Second Law could be violated?

Postby Charlie! » Tue Apr 28, 2009 2:13 am UTC

Yakk wrote:The thing is, entropy increase can also be described as information increase. It takes more bits of information to describe a room in which all of the particles of air are spread out, than one in which all of the particles are in a corner.

Hm, two problems with these sentences.
1) particles in a corner has the same entropy (same number of microstates available) as particles in the whole room as long as the whole room is available to the particles.
2) particles in the corner takes the same amount of information (3 numbers per particle) as particles over the whole room.

Lastly, I think it's time to tackle my suspicions about this common "information is entropy" claim:

Entropy is related to the log of the number of microstates available, which in turn is related to the number of particles raised to the volume. So you end up with something proportional to the volume and to the log of the number of particles. Information, on the other hand, if you just need 3 numbers per particle, should be linearly dependent on the number of particles in the box, not log(n) dependent. So I THINK (maybe) that the math doesn't think entropy and information are the same.
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Re: What if the Second Law could be violated?

Postby BlackSails » Tue Apr 28, 2009 2:41 am UTC

Charlie! wrote:
Yakk wrote:The thing is, entropy increase can also be described as information increase. It takes more bits of information to describe a room in which all of the particles of air are spread out, than one in which all of the particles are in a corner.

Hm, two problems with these sentences.
1) particles in a corner has the same entropy (same number of microstates available) as particles in the whole room as long as the whole room is available to the particles.


Its not how many microstates are available, its how many microstates describe the current macrostate. So for all the particles in the corner, there is only 1, while there is roughly a kajllion for the usual macrostate.

Imagine I roll two dice and tell you their sum. If I tell you the sum is 2, you know with perfect certainty that I rolled (1,1). Thats 1 microstate, and so there is no entropy.

Now lets say I tell you I rolled a sum of 4. I could have (3,1)(2,2)(2,2)(1,3). The entropy is ln(4)

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Re: What if the Second Law could be violated?

Postby Charlie! » Tue Apr 28, 2009 3:00 am UTC

BlackSails wrote:
Charlie! wrote:
Yakk wrote:The thing is, entropy increase can also be described as information increase. It takes more bits of information to describe a room in which all of the particles of air are spread out, than one in which all of the particles are in a corner.

Hm, two problems with these sentences.
1) particles in a corner has the same entropy (same number of microstates available) as particles in the whole room as long as the whole room is available to the particles.


Its not how many microstates are available, its how many microstates describe the current macrostate. So for all the particles in the corner, there is only 1, while there is roughly a kajllion for the usual macrostate.

Oh, okay. I see what he was saying. I was busy looking at it through the wrong lens.
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Re: What if the Second Law could be violated?

Postby Forum Viking » Tue Apr 28, 2009 3:33 am UTC

BlackSails wrote:
Forum Viking wrote:
frezik wrote:The second law is a strange exception to the usual laws, in that it's based on probability rather than absolutes. For instance, it is theoretically possible for all the oxygen molocules in the room to organize themselves into one little corner. Such a room would have "broken" the second law by being more organized, but it's so unlikely to happen that we discount it entirely.

I suspect that a universe where the second law could be violated would have some frelled up laws of probability to go with it.
Infinite limits! Yay! Entropy's a weird, and cool thing. It almost seems that if we had a big computer to keep track of everything, then there would be no entropy. I think the refutation is that the computer would have to keep track of itself, and this is for some reason impossible.


You can also refute it with QM. In QM, not only is the future position and momentum of a particle indeterminate but the past trajectory is as well

Ah yes, Quantum Mechanics.
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Re: What if the Second Law could be violated?

Postby airplanespaceship3 » Sun May 10, 2009 4:01 am UTC

I recently had a physics problem about how much total energy is locked away in the irretrievable form of heat in the oceans, atmosphere, and upper 10km of crust. Turns out, if you could violate the 2nd law, you'd be able to meet modern civilization's power needs for millions of years off that ambient heat energy alone. That's without considering the fact that any work you proceed to do will re-heat the surroundings. And refrigenerators and AC-A/C's would be the most kick-ass inventions ever. If SLTD could be violated, I'd say the biggest practical effect would be an upheaval of current energy politics/economics. Any ideas on how that would play out?
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Re: What if the Second Law could be violated?

Postby Link » Sun May 10, 2009 4:33 am UTC

airplanespaceship3 wrote:Any ideas on how that would play out?
Electricity would become very very cheap, if not free. Gas and such would disappear from everyday use since electricity will be the way to go. I imagine paper batteries would soon become very popular. With free energy available, technological research will be vastly accelerated. Within 10 years, there'd be MagLev roads and cars and even the poorest of all people would have access to technology vastly superior to what we have today, and within 50 years, technology will have advanced into things we can only dream of now. Before more efficient ways of transport are found, the skies will be littered with ultracapacitor-powered planes, and today's driver's licences will be personal helicopter licences. Tesla's wireless electricity may also finally be realised; who cares about losses when you can recollect them?

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Re: What if the Second Law could be violated?

Postby evilbeanfiend » Sun May 10, 2009 7:11 am UTC

if the second law could be violated then the robots would run wild!
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