Proof for the 2. Law of thermodynamics ?

[Abstractness]

I've seen thought experiments like Maxwell's demon, which seem to break the 2. Law of thermodynamics. Most of those thought experiments have been refuted.
My question:
Is there a mathematical proof of the unbreakability of this law?
Are Physicists even trying?

 

[russ_watters]

I've seen thought experiments like Maxwell's demon, which seem to break the 2. Law of thermodynamics. Most of those thought experiments have been refuted.
My question:
Is there a mathematical proof of the unbreakability of this law?
Are Physicists even trying?

Welcome to PF!

You're mixing a couple of separate things here. A mathematical proof is just proof that the math works. It doesn't prove the physical reality of what the math predicts. That's done with experiments.

That said, there really isn't much overt effort to prove/disprove the laws of thermodynamics. They are far too fundamental to be actively questioned. But fear not: every time you plug in a refrigerator or start your car, you are performing an experiment that proves the laws of thermodynamics correct.

 

[Abstractness]

Welcome to PF!

You're mixing a couple of separate things here. A mathematical proof is just proof that the math works. It doesn't prove the physical reality of what the math predicts. That's done with experiments.

That said, there really isn't much overt effort to prove/disprove the laws of thermodynamics. They are far too fundamental to be actively questioned. But fear not: every time you plug in a refrigerator or start your car, you are performing an experiment that proves the laws of thermodynamics correct.

If you take the Standardmodel as axioms, has it mathematically been proven that it is impossible to build a machine of any kind, which breaks the second rule of thermodynamics? I mean, Someone could try to build one using nanotechnology.

 

[DrewD]

If you take the Standardmodel as axioms, has it mathematically been proven that it is impossible to build a machine of any kind, which breaks the second rule of thermodynamics? I mean, Someone could try to build one using nanotechnology.

The Standard Model might be a little much, but from basic QM and information theory Wiki says. I recall seeing this stated and it seemed to make sense.

 

[russ_watters]

If you take the Standardmodel as axioms, has it mathematically been proven that it is impossible to build a machine of any kind, which breaks the second rule of thermodynamics?

Yes. Are you familiar with, for example, Carnot's theorem?
http://en.wikipedia.org/wiki/Carnot's_theorem_(thermodynamics )

I mean, Someone could try to build one using nanotechnology.

People can try whatever they want, but scientists are not in the habit of trying things they know won't work.

 

[Abstractness]

Yes. Are you familiar with, for example, Carnot's theorem?
http://en.wikipedia.org/wiki/Carnot's_theorem_(thermodynamics )

Afaik Carnot assumed that we can't observe or manipulate single particles, because they're too small. But today this assumption doesn't match reality anymore. So it would be natural to assume that the second law of thermodynamics could be broken using nanotechnology. For example using Maxwell's Demon. But this machine has been refuted too. So is it really impossible to build a nano scale machine which violates the 2.law ? idk. but in the answer of DrewD there's a reference to a thesis which claims to prove the 2.law based on the 'true' randomness in quantum physics.

 

[russ_watters]

Afaik Carnot assumed that we can't observe or manipulate single particles, because they're too small. But today this assumption doesn't match reality anymore.

True.

So it would be natural to assume that the second law of thermodynamics could be broken using nanotechnology.

That's not natural at all. Natural is assuming consistency.

 

[Abstractness]

True.

That's not natural at all. Natural is assuming consistency.

Ok, then it's only natural for James Clerk Maxwell and me.

 

[russ_watters]

Ok, then it's only natural for James Clerk Maxwell and me.

Oy, so now you're in the company of Maxwell? I doubt Maxwell would still hold that position if he hadn't died 100 years ago.

 

[Zarqon]

I mean, Someone could try to build one using nanotechnology.

Here's a link to a quantum heat engine (click), which uses a single ion to implement an Otto cycle. I don't think it breaks the 2nd law of thermodynamics...

 

[DrewD]

Ok, then it's only natural for James Clerk Maxwell and me.

I don't think it was natural for Maxwell. The demon makes the point that there is a statistically insignificant chance that the entropy will decrease. He was right. The demon is sort of a silly way of talking about it since it is a mechanism that does not follow the laws of physics. While there is always a possibility that certain laws of physics will be overturned, it is very unlikely that introducing subsystems that follow the second law will make the larger system not follow the second law.

As a side note, the refutation of Maxwell's demon uses only the fact that a measurement is made. Therefore, there would have to be a mechanism that can lower entropy without knowing where the particles are... which more or less brings us back to Carnot.

 

[Khashishi]

The second law of thermodynamics is a law of nature and not a law of mathematics. You can't mathematically prove it.

 

[DrewD]

The second law of thermodynamics is a law of nature and not a law of mathematics. You can't mathematically prove it.

But some laws of nature can be mathematically derived from others which allows us to narrow the laws of nature down.

 

[Abstractness]

LOL, Now they're going to try to build Maxwell's demon again: http://www.kurzweilai.net/infernos-project-maxwells-demon-in-nanoscale-systems

 

[DrClaude]

The second law of thermodynamics is essentially a statistical law. In the thermodynamic limit (big system), probability distributions are so narrow that at equilibrium a system will always be found in the state of maxium entropy. However, for small systems, fluctuations are important and, especially for transient processes, you can have behaviours that go against the second law, where the entropy is (at least temporarily) reduced. But as soon as you consider the "bigger picture" (including all the apparatus necessary for creating a Maxwell demon), you'll find that entropy is always increasing.

 

[dauto]

The Maxwell Daemon cannot be built using nanotech (or any other tech) because the daemon itself is also under the laws of thermodynamics. Feynam has an excellent - as usual - discussion about that topic in his lectures. He goes into details explaining why a specific hypothetical implementation of the daemon wouldn't work. In that implementation there is a ratchet that would prevent the atoms from leaking back in the opposite direction. He showed that the ratchet would over heat and stop working before any violation of the 2nd law was achieved. That is true for any other conceivable mechanism as well.