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Maxwell's demon

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Marko

Wed Oct 17 2007, 01:23PM

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

Hello all.

I got especially eager and intrigued after reading some bjorn's posts... I hope you guys have nothing against this type of thread.

As we all know, the genuine Maxwell's demon fails because it always loses more energy for measurement than it can recover by running a heat engine from now decreased-entropy system.

Now, my question is rather simple, what if it doesn't?

The energy-wasting measurement system is replaced with a quantum-mechanically random timer which opens the ''trap door'' for a short, random length interval.

Timer needs to use, but only very small amount of energy as I think which is by no way connected to final produced energy.

So it is now by pure chance whether will entropy increase or decrease, and there is no possible physical way to control the outcome.

It is enough to view the system as purely classical, only the randomness generator being based on QM.

If this doesn't look bad enough, if we (hypothetically) scale the experiment up, and say that particles have enormous (probably big-bang like) energy density, we could build a macroscopic PM of second kind.

Note that I used only classical approach, no conservation of momentum violating cold-to-hot energy transfer and etc.

It now seems that it is purely a matter of miracle whether it will happen or not, and nothing controls it.

You may say that it will average out after million of such experiments but to me it seems like poor argument.

If it was like so we should see violations of second law everywhere, yet it is so omnipotent and right. It is often said that 2.nd law is approximation , but to what extent? What defines the limit?

What *really* stops us from creating a macroscopic 2.nd kind perpetual motion so stubbornly?

Marko

Hazmatt_(The Underdog)

Wed Oct 17 2007, 07:21PM

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

Maxwell's Demon fails because it requires a trap door with NO mass in order to operate. A material with no mass cannot stop a particle, its impossible, which I've known for years but wasn't totally sure about it until a Physicist at my college talked about Maxwell's Demon at one of our little get-together Physics Club meetings.

Marko

Wed Oct 17 2007, 09:41PM

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

Why zero? I don't see any reason and it's first time I hear this. It could have miniscule but nonzero mass and require very little energy to operate, still it would statisfy.

You could also imagine that box is made of solid that is in thermal equilibrium with everything too, it doesn't hurt the experiment.

As I know, everyone states that measurement is only problem here.

Hazmatt_(The Underdog)

Wed Oct 17 2007, 10:39PM

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

Maxwell's demon assumes no energy is consumed to move the trap door. To satisfy that the door must be mass-less. If the door has mass then you must do work to move the door, which is going to consume the energy you gain while moving the particles around.

AndrewM

Thu Oct 18 2007, 12:34AM

Registered Member #49 Joined: Thu Feb 09 2006, 04:05AM
Location: Bigass Pile of Penguins
Posts: 362

You're treating this as an engineering problem, when it is actually more elegant than hinges and doors. One can always imagine a thinner and thinner door until the energy required to move it is less than the average energy "available" from a single particle passing through it.

The demon fails because it can be shown that more energy is expended in observing the particles and timing the opening of the door than could ever be carried by said particles.

Marko's supposition about exploiting the behavior of random walks is interesting; you can simplify his thought experiment by removing all features except for a volume of gas. In any such volume, random particle motion will set up and destroy gradients in the volume spontaneously. I can't really say why this is due to fail, however it sounds much like gambling; even if you always sell high, you'll still run out of money at some point.

Bjørn

Thu Oct 18 2007, 12:10PM

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

It is often helpful to view Maxwell's demon as three processes. Observation, computation and actuation.

If we heat up the particles so they each contain a lot of energy we find each process of the demon also requires more energy. If the particle moves faster we need to send out more photons to observe it earlier so we can to the other two processes in time. The computation will require more energy because it needs to be faster and the noise level increases. The actuation will require more energy since the mechanism must be faster and more solid.

The second law of thermodynamics does not seem very fundamental at all. No matter how you look at it you soon reach an assumption that does not have a deep theoretical basis. Sooner or later big bang will enter the explanation in some way. It seems like a hidden anthropic principle, it holds true because we exist to question it. The foundation of the law is weak, but the accuracy on a large scales is extreme.

To get a sense of the statistical nature of the law, try to imagine it with only two particles and count how many are on each side of the box at given instants, then keep adding more and more particles. With just 100 particles there are 2^100 different ways the particles can be configured if we divide the box in two halves. Only two of those configutrations involve all particles being on one side or the other. To make matters worse therer will be a pressure gradient when more particles are in one side of the box so those two configurations are the least likely by far to be entered by random chance.

Marko

Thu Oct 18 2007, 02:06PM

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

The foundation of the law is weak, but the accuracy on a large scales is extreme.

That's how paradoxical this thing is - you can only violate the second law if a pure miracle allows it to you.

Still, it's never violated on macroscopic scales.

What really distinguishes microscopic from macroscopic anyway?

I have found some non-canonical evidence that some scientists use this to explain low entropy past of the universe, that such a demon could have happened in reality very moments after big bang (setting off all the symmetry breaking stuff I know nothing about).

It is hard to even think about something like that happening in universe again, and I would probably get bashed by scientists if I said 'entropy of the universe just sometimes decreases if it likes it so'.

No matter how low the chance may be, such an implication still looks very bizzare.

Bjørn

Sat Oct 20 2007, 06:35AM

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

What really distinguishes microscopic from macroscopic anyway?

1. The system is always microscopic because at every instance there will be an inequality.
2. The system is always macroscopic because given enough time the inequalities cancel each other out.

I think that leave us with a classical measurement paradox. You can always point out examples that are clearly one or the other from a particular viewpoint but you can't point out exactly where the border is. The answer depends as much on the observer as on the properties of the system in question.

What usually saves us is the truly gigantic difference in volume there is between clearly microscopic and what we normally consider "small". So practically every useful system can be considered macroscopic.

This does not answer the question in an absolute sense, it just opens the door for some new interesting questions.

Marko

Sat Oct 20 2007, 02:33PM

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

So.. from macroscopic point of view;

It ''could'' happen for the 2nd law to get violated;

But there is no way we could affect or predict it, it's a pure matter of luck;

..and all we could do is build an apparatus that will increase the chances for such an outcome - miracle can come only on it's own?

WaveRider

Sun Oct 21 2007, 03:37PM

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

This is an extremely interesting topic!

Yes. entropy can be seen to decrease "locally" while the overall (closed) system entropy must always increase. I recommend looking at the so-called "fluctuation theorem" for an explanation as to how this can happen.

A couple of interesting points:

The second law is not "theoretically weak" or somehow "magic". It is a mathematical statement about how much information we need to completely describe the system under study. Put another way, given what we can measure or observe, how many possible states will give this observation? This is the notion of "multiplicity of states" that Boltzmann used in his famous statistical description of entropy.
Even the conservation of energy (the first law) can be viewed as a statistical relationship. Fluctuations can cause local violations, but on average the law will always hold. Quantum fluctuations allow temporary violations as long as the Heisenberg uncertainty relationship is not violated, i.e. delta t x delta E < h/2pi
Maxwell's demon fails on a couple of counts (IIRC). 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". He can't see the particles to separate them! The act of observation requires a non-equilibrium event to take place (absorption or emission of a photon, for example)
The door could be (essentially) massless in the sense we could imagine some type of "force field". However, this immediately implies some external energy source would be needed to switch this force field on and off. Again, we are no longer in equilibrium.
Closer to home to an electronics enthusiast: A diode is a device that essentially "sorts" electrons depending on the direction of their movement. Why does a diode not produce current when thermal action spontaneously can produce electron-hole pairs in its depletion region at room temperature.? Under what circumstances will we observe the diode produce a net current?

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