Does random have rules?

[Alex K]

the second law definitely holds only on average for large enough systems, and for finite systems there is a small chance that they are violated. It's just that for macroscopic systems this probability is unmeasurable small.

Typical example: if you have a box full of gas molecules, there is the slim chance 2^-N that at some point in time they will all sit in the left half of the box, which would correspond to a state of much lower entropy than the starting state.

[watchamadoodle]

the second law definitely holds only on average for large enough systems, and for finite systems there is a small chance that they are violated. It's just that for macroscopic systems this probability is unmeasurable small.

Typical example: if you have a box full of gas molecules, there is the slim chance 2^-N that at some point in time they will all sit in the left half of the box, which would correspond to a state of much lower entropy than the starting state.

(I'm probably going to get the details all wrong, but hopefully you can decipher the essence.)

It seems like the slim chance of all the gas molecules being in the left half of the box would require a simultaneous observation of all those particles? Maybe some of the thermodynamic laws can be restated to say that such an observation is illegal?

If the whole universe was just two particles in their probability wave state, then it seems like the entropy of the universe might be the sum of the variances of the two probability waves? If the two probability waves have a single narrow peak, then the entropy would be lower than if the probability waves were more diffuse?

At some point the particles collide or observe each other and their probability waves collapse? Then there are two new probability waves with new entropy values?

Does thermodynamics work with such a simple system?

[Alex K]

the second law definitely holds only on average for large enough systems, and for finite systems there is a small chance that they are violated. It's just that for macroscopic systems this probability is unmeasurable small.

Typical example: if you have a box full of gas molecules, there is the slim chance 2^-N that at some point in time they will all sit in the left half of the box, which would correspond to a state of much lower entropy than the starting state.

(I'm probably going to get the details all wrong, but hopefully you can decipher the essence.)

It seems like the slim chance of all the gas molecules being in the left half of the box would require a simultaneous observation of all those particles? Maybe some of the thermodynamic laws can be restated to say that such an observation is illegal?

That's largely correct - let's stay in the classical realm for a moment; there, observation is not forbidden. But - the energy you would need to expend to observe these guys to know when to shut the box in the middle to preserve them on one side, outweighs the usable energy you could draw out of this in violation of the second law. But it's a very subtle argument.

JC Maxwell and friends already thought about this in detail:

http://en.wikipedia.org/wiki/Maxwell%27s_demon

If the whole universe was just two particles in their probability wave state, then it seems like the entropy of the universe might be the sum of the variances of the two probability waves? If the two probability waves have a single narrow peak, then the entropy would be lower than if the probability waves were more diffuse?

At some point the particles collide or observe each other and their probability waves collapse? Then there are two new probability waves with new entropy values?

Does thermodynamics work with such a simple system?

I think it's problematic. Maybe they will approach something like a thermal energy distribution if you average over very long times. But generally I'd say thermodynamics doesn't really apply.

[watchamadoodle]

If the whole universe was just two particles in their probability wave state, then it seems like the entropy of the universe might be the sum of the variances of the two probability waves? If the two probability waves have a single narrow peak, then the entropy would be lower than if the probability waves were more diffuse?

At some point the particles collide or observe each other and their probability waves collapse? Then there are two new probability waves with new entropy values?

Does thermodynamics work with such a simple system?

I think it's problematic. Maybe they will approach something like a thermal energy distribution if you average over very long times. But generally I'd say thermodynamics doesn't really apply.

Hmmmm. I wonder if we defined a property of probability waves (similar to variance) and call that "QM entropy". Maybe we could tinker with the definition of "QM entropy" until thermodynamics works at the QM level with a small number of particles. Then wouldn't it be neat if we could prove mathematically that this "QM entropy" scales-up to the entropy in steam engines and so forth?
(I like to day dream. )

[Alex K]

Sure it's a valid thought. The existing concept of entropy of quantum systems I know however always gives you entropy S=0 for pure quantum states before wave collapse.

http://en.wikipedia.org/wiki/Von_Neumann_entropy

It only gives nontrivial values if on top of the quantum uncertainty you add traditional probabilistic uncertainty by going from a pure to a mixed quantum state.

[Anomalocaris]

I think it's problematic. Maybe they will approach something like a thermal energy distribution if you average over very long times. But generally I'd say thermodynamics doesn't really apply.

Hmmmm. I wonder if we defined a property of probability waves (similar to variance) and call that "QM entropy". Maybe we could tinker with the definition of "QM entropy" until thermodynamics works at the QM level with a small number of particles. Then wouldn't it be neat if we could prove mathematically that this "QM entropy" scales-up to the entropy in steam engines and so forth?
(I like to day dream. )

what does scale up mean? Solving all the correct probabilistic wave function would result in 2nd law of thermal dynamics as a natural outcome?

That seem to me to imply probability waves are non-local and/or systematically evolve by themselves over time.

[Drich]

After reading this I was going to make room for you on the pedestal I have placed Equal-lax, as being one of the smart ones.. But then You said this, and claimed it made sense... Which means you probably and pasted your questions from Somewhere..

Not a cat person? hock:

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Randomness is a concept. It has whatever constraints and rules you attribute to the concept. Particular physical phenomenon may behave in a way which correspond to particular versions of randomness subject to constraints and rules associated with that version.

Would you say that about mass or energy and so forth?

Actually i am, I just like mine bulgogi style

[Anomalocaris]

Which explains how you come to have crispy fried dumplings for brains.

[downbeatplumb]

Which explains how you come to have crispy fried dumplings for brains.

Are you implying that Drich has brains? This seems to be unsupported by the evidence.

[Alex K]

what does scale up mean? Solving all the correct probabilistic wave function would result in 2nd law of thermal dynamics as a natural outcome?

Well that's a good question. In this case one would have to apply some concept of decoherence to end up with a classical statistical system. And one would try to carry over the quantum definition of entropy and see where one ends up.

The v.Neumann Entropy concept for mixed quantum states I linked to above can be relatively easily become classical Entropy if one plugs in a suitable mixed state corresponding to a classical statistical mixture. The difficult part is really seeing how this mixed state arises out of a big quantum system. Yep, understanding decoherence is the difficult part.