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Maxwell's demon

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Hazmatt_(The Underdog)

Sun Oct 21 2007, 07:12PM

Registered Member #135 Joined: Sat Feb 11 2006, 12:06AM
Location: Anywhere is fine
Posts: 1735

When the diode is a solar cell.

Bjørn

Sun Oct 21 2007, 11:48PM

Registered Member #27 Joined: Fri Feb 03 2006, 02:20AM
Location: Hyperborea
Posts: 2058

The second law is not "theoretically weak" or somehow "magic".

The second law is not fundamental and while obvious is not supported by a proper theoretical framework. It is just an assumption that "Heat flows from a hotter to a colder body" from which some formulas have been created that gives the correct answers. The first law is supported by a much deeper theoretical framework and can be considered fundamental in a completely different way.

While the formula itself as a mathematical statement is correct it does not have a proof based on more fundametal principles and its relationship to reality is unclear.

Coyote Wilde

Mon Oct 22 2007, 04:55AM

Registered Member #175 Joined: Tue Feb 14 2006, 09:32PM
Location: Sudbury, ON
Posts: 111

There was a mathematical physicist, whose name escapes me, who put forth a paper a while back which offered a 'proof' that the Second Law had to exist in any self-consistent physical framework with laws remain consistent over time (ie, F=ma today is still F=ma for the next 2 billion years). Which sounds like a pretty good theoretical basis to me, if a proof it actually was. I'll try and find a reference for that.

Bjørn

Mon Oct 22 2007, 06:02AM

Registered Member #27 Joined: Fri Feb 03 2006, 02:20AM
Location: Hyperborea
Posts: 2058

I would really like to see it because I have never found anything that is close to proving that Maxwell's demon really is fundamentally impossible. Hardly a single of the definitions takes quantum mechanics into consideration even if it surely is fundamental to the final answer. Gravity might also play an important part in some cases.

First, if the observer uses no energy, he must by definition be in equilibrium (at the same temperature) as the boxes with the particles he wishes to separate. He will, in fact, be unable to "observe" the particles because the radiation temperature of the boxes will match his own, hence he will "see" only a homogeneous radiation background equal to his eye's own "noise".

Yes, it clearly shows that the demon must spend some energy. The problem is that a working demon will build up a temperature difference and have energy to spend. Then it becomes a problem to show that it can't work for any of an infinite combinations of matter, fields and energies.

It is impossible to fault the second law of thermodynamics but at the same time it is very hard to show clearly why.

Steve Conner

Mon Oct 22 2007, 09:46AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Well, the second law of thermodynamics is a synthetic truth, equivalent to a statement like "All crows are black". It's not a proper analytic truth like 2+2=4. Some smart professor type (Kelvin, Carnot or Clausius, I forgot who) just thought it up to explain experimental results, and then we apply it by induction to everything else.

No experiment has yet been found that gives results that would disagree with the Second Law. So we say: "Every crow we ever saw was black, so all crows are black."

The problem is that people are so fond of this process of induction, that if they got results that disproved it, they would just assume they made a mistake. Or their peers certainly would when it came time to publish! Look what we do to free energy nuts here. So, we go on to say: "All crows are black, and anyone who says they saw a white one with purple polka-dots is crazy."

I personally like to equate the Second Law to the anthropic principle. Darwin said that evolution was driven by competition for finite resources. Maybe in a universe without the constraint on resources imposed by the Second Law, consciousness couldn't have evolved to the point where it could ponder the Second Law. But that is speculation of an even less provable nature!

WaveRider

Mon Oct 22 2007, 09:48AM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

I believe it was Sadi Carnot who discovered something fundamental was missing from the formulation of thermodynamics of his day. He realised that all heat engines have some built in irreversibility that required another quantity in the formulation..... While he did not postulate entropy directly, his caloric theory led to Clausius and Kelvin to develop the idea of entropy and formulate the second law.

About as close as one can get to a "proof" of the second law is Boltzmann's H-theorem based on ideas of statistical mechanics and kinetic theory. It has its share of problems and contradictions of course (does not address time-reversal symmetry or poincare's recursion problem for closed newtonian systems).

There is nothing any less fundamental than energy conservation going on here.. While it lies outside the usual "fundamental" conservation laws (mass, charge, momentum and energy...to quote only the classical ones), it hints at a fundamental limit to how much we can know about a system...much like Heisenberg's postulates about quantum mechanical systems... As the system phase trajectory evolves, it becomes "smeared out" as the system "loses it memory" as a result of "molecular chaos" (to use Boltzmann's term). (EDIT:This is the magic assumption that Boltzmann used to break time-reversal symmetry...) On one hand this implies an appeal to the anthropic principle in the sense that it is our limits as observers that prevent us from knowing the system state to infinite precision...but a deeper anaylsis would say that perhaps it is the nature of small particles to scatter with a range of uncertainty that breaks time-reversal symmetry. But then again, as conscious observers, we can never break out of the anthropic bias.....this is getting beyond my capacity as armchair philosopher

......

Physical laws are usually resistant to rigorous proof (much to the dismay of mathematicians). Maxwell's electrodynamicss, Newton's (Einstein's) laws, Quantum mechanics are all heuristic constructions based on experimental observations. Proofs of self-consistency exist...up to a point, but nothing exists to say that they are fundamentally the whole story.......

Bjørn

Wed Oct 24 2007, 08:18AM

Registered Member #27 Joined: Fri Feb 03 2006, 02:20AM
Location: Hyperborea
Posts: 2058

What I have managed to dig out is that the Landauer-Penrose-Bennett solution is fairly solid in putting a stop to Maxwell's demon in the from and scale we have been discussing.

It also seems that a "demon process" that does not concern indicidual particles but use fields, forces or special geometry on a larger scale to break the second law is still an open question.

Marko

Wed Oct 24 2007, 02:45PM

Registered Member #89 Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145

Awesome replies over there guys..

So, it ends up that SLOT is stable for any attempt of direct violation, but can only be violated spontaneously by a roll of a dice? No arrangement of matter can violate it willfully and continuously.

I replaced the 'classical' demon with a system which needs to use only small non-zero amounts of energy to toss the dice and open the door which doesn't depend by possible energy gain from entropy decrease.

If that isn't enough I go for andrew's proposal, the gas tosses it's own dice and may decrease the entropy spontaneously.

So, we really haven't seen apparent violation of SLOT just because we ''haven't looked hard enough''?

From plentitude principle we could expect some major violations but still completely unpredictable.

Yes. entropy can be seen to decrease "locally" while the overall (closed) system entropy must always increase.

Why? From all this I don't see why entropy of enitre universe at some wouldn't decrease a bit through some crazy chain of events.

Of some isolated closed system close to equilibrium, far more easily.

What you mean as ''locally''?

WaveRider

Wed Oct 24 2007, 03:19PM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

Marko,
I suppose it is statistically possible that the entropy of the universe could decrease, but the probability of seeing such a situation is so astronomically small that you may as well say that it will never happen.. (I know...such an answer is very unsatisfying...but all evidence seems to point that way...)

"Local" means "small system" in the sense of what ever we can dream up. Magnetising a piece of iron can decrease the entropy of the iron dipole-field system (the local part) but the entropy of the universe (the battery/generator/power supply/iron/field system together) actually increases....

Marko

Wed Oct 24 2007, 04:14PM

Registered Member #89 Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145

So.. I got impression that my idea of ''dice throwing maxwell's demon'' actually works so I can move further.

There are certain theories I may have started to understand further;

Universe is thought to have emerged from a singularity that was extremely hot(???), but still high entropy state like 'normal' black holes; but, normal holes are cooler more massive they are. So how did the universe get into the low entropy state? Looks like direct violation of 2.nd law.

What really makes this singularity different? (if question makes sense?)

It's no wonder that it's among 'unsolved problems' in wikipedia.

Now it appears that fluctuation theorem is what lowered the entropy *after* that... and to great extent since energy was very dense. If I understood it right.

Then I hear buzz words like ''symmetry breaking''. What can symmetry breaking really do for this matter? I got completely lost in particle physics jargon.

Wouldn't involvement of anything but fluctuation theorem imply that universe is an open system?

Or from the other side it would imply possibility of building SLOT-violating machine (''real'' demon) which I'm not happy with either.

Marko

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