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Cool Thought Experiments I: Maxwell's Demon
By Garth Sundem | February 2nd 2009 12:28 PM | 16 comments | Print | E-mail | Track Comments
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About Garth Sundem

Do you need a Monday morning shot of geekery?

If so, you've come to the right place. Every Monday, early, I'll drop splendid geekery from the fields of physics, math, computer science, zoology


... Full Bio

Throughout history, scientists, philosophers, mathematicians and Phd students lacking funding for actual research have turned to the thought experiment in hopes of discovering something publishable, thereby retaining tenure and/or attracting the admiration of comely undergraduates. The best thought experiments throw light into dark corners of the universe and also provide other scientists, philosophers, mathematicians and destitute Phd students a way to kill time while waiting for the bus.

Below is a classic thought experiment, pillaged from my book The Geeks' Guide to World Domination (Be Afraid, Beautiful People). I'll post a new thought experiment each day this week.


Maxwell’s Demon

The Second Law of Thermodynamics states that a system will never spontaneously move toward a higher degree of order. It takes energy to increase order.

But, imagine you had a box filled with molecules, vibrating away at various speeds and creating by their interaction a constant temperature inside the box. Now, stick a divider down the middle of the box, splitting it into two chambers. In this divider is a tiny door operated by a demon (potentially Dick Cheney). The demon opens and closes the door, allowing faster (hotter) particles to bounce naturally into the right chamber and slower (cooler) particles to bounce into the left chamber. Over time, the order of the system is increased—the right chamber gets hotter and the left chamber gets cooler. Remember, the demon has added or subtracted nothing from the system, only opened and closed a door, thus allowing particles to pass through on their natural paths.

Does this violate the Second Law of Thermodynamics? What d'you think?

Comments

Nope, because it's part of a greater system. If you think you've violated the Second Law, then ten times out of ten your view of the "system" is wrong, and you must factor for other components of said system.

ME (not verified) | 02/02/09 | 14:43 PM
Garth Sundem's picture
Cool. Are you saying that the box itself can't be evaluated independently of the surrounding system? The table it sits on, that atmosphere around it, the frickin' demon sitting atop? How does this greater view of the system restore the Second Law? Of course, I'm playing demon's advocate a bit here...

Garth Sundem | 02/02/09 | 14:51 PM
The door takes energy to open and close; Therefore, energy is being added to the system.

Antigravity (not verified) | 02/02/09 | 15:11 PM
Garth Sundem's picture
True, but has the door's energy actually been used to decrease the system's entropy? Remember, the particles' paths haven't been altered in any way. The door might as well have been opening and closing in a random pattern, right? In this model, the door would have let equal numbers of particles into both sides (like a semi-permeable membrane in basic diffusion), thus leaving the system's perfect entropy in tact. So, does the door's motion necessarily affect the system's entropy?

Hmmmm....

Garth Sundem | 02/02/09 | 15:25 PM
The demon is part of the system, so all energy that the door uses has to be coming from the demon, which in turn either eats apples or something from a even larger system or becomes tired.
Either way if he eats all the apples he can't keep operating the door without violating the 2nd law unless the apples in some way can collect the energy transferred to the box from the demon.

Nuno Cravino (not verified) | 02/02/09 | 15:28 PM
Garth Sundem's picture
Yep. That's my answer, too. Are there other answers? Either way, you've also reconfirmed my suspicions concerning demons' consumption of iPods, Steve Jobs and the operating platform in most direct competition with PC. (You didn't mean the fruit, did you?)

Garth Sundem | 02/02/09 | 15:38 PM
Well now all we have to do is ask Dick Cheney whats the latest tune in his iPod, and warn him(not) of the dangers of compulsive iPod eating.

Nuno Cravino (not verified) | 02/02/09 | 15:47 PM
Garth Sundem's picture
I think Cheney documents well the dangers of compulsive iPod eating...His procedures are no longer termed "bypasses", rather, they're "work arounds".

Garth Sundem | 02/02/09 | 15:58 PM
Garth Sundem's picture
Oh, and don't forget to join me tomorrow morning for Thought Experiments Round II. I've got a goody on tap.

Garth Sundem | 02/02/09 | 16:31 PM
Hank's picture
We had an interview a while back with Dennis Bushnell, chief scientist at NASA, who is not entirely sure the 2nd Law is a Law.  Maybe it's just more of a Zero Point Energy guideline.   Maybe it's even the answer to energy problems.

So maybe he's the demon in the box.   That would sure feel better than having Dick Cheney in charge of it.

Hank Campbell | 02/02/09 | 17:40 PM
Garth Sundem's picture
That's very, very cool. With all sortsa cool implications, like the origin of life.

Garth Sundem | 02/02/09 | 17:49 PM
No, it doesn't violate the second law of thermo at all, or the first. There is nothing from stopping one chamber from getting hotter and the other getting colder, much like an ice cube and a cup of coffee. If you put an ice cube in a cup of coffee, the ice melts,but if the ice got colder and the coffee got hotter no laws would be violated. Taking the demon chamber example there is a possibility of this happening simple statistics can tell you that. I have ten particles and I am choosing five of them to be put in one chamber, but not just any five, five faster(red)(hotter) particles to be in that chamber.The odds are not that high for all the faster particles to go into the chamber but still a chance. So why don't we see this in real life? Well lets add more particles to the chambers, say 6.022 x 10^23 particles, Avogadro's number,of faster particles and slower particles. The odds of all 6.022 x 10^23 faster particles going into one side of the chamber and all the slower particles going into the other side is super unlikely, not likely enough any human will observe it and that is why we don't see this in real life. So it is possible for one of the two chambers to get colder and one chamber to get hotter, it is just unlikely. I hope that was somewhat answering the question.

Marc Doyle (not verified) | 02/02/09 | 18:55 PM
But how does the demon know which particle is hotter than the others?
He should measure the energy a particle to decide whether opening the door or not, and that requires an interaction with a particle, or the emission of one, for example, a photon. Indeed, the demon should have to "scan" at least the boundaries of the door for particles. Even more, to be sure which one has to go which way, the demon has to know the difference of energies, which now requires an interaction with at least two different particles. The interaction with or emission of a particle (there will be a recoil for momentum conservation in emission) will also change the energies of the "scanned" particles, and this process must be measured by the demon, supposedly outside of the system, now a kind of Deux ex Machina. The bottom line: decision requires information, which takes energy flow.
This implies the system is not closed now, so second law of thermodynamics cannot be applied.

David Ordenes (not verified) | 02/03/09 | 20:03 PM
Gwynn Gates's picture
I propose that the door guarded/controlled by the demon will eventually get overloaded.  Are the molecules moving in a truly spontaneous manner if in both chambers there is only a small opening made available for them to travel through each time?  They are going to travel through whatever is available but is that spontaneous or slightly choreographed by the demon?  Plus, they are traveling through in opposite directions simultaneously so how many are colliding at the threshold?  Not to mention, some may be bouncing over in the corner and never reach the door.  What happens to the demon when the power of the gate/door becomes too much for it to handle?

Gwynnedd Stone | 02/04/09 | 14:59 PM
Garth Sundem's picture
At that point the demon goes through the door, crossing the threshold from its world to ours. The only way to return the demon to the proper side of the door is by trapping it in a Schrodinger Box. If this fails, the demon takes the form of whatever you first think of. God, please don't let it be Dick Cheney. Or the Pillsbury dough boy.

Garth Sundem | 02/04/09 | 16:21 PM
Maxwell's demon is a decision-making device, a data-handler. Every decision-making process consumes energy.

The only energy in the box potentially available for decision-making is the temperature difference between hotter particles and colder ones. In order to use that energy difference as a power source, it must first be detected. However, the detection process requires energy! The circle is closed.

Maxwell's demon would have to operate outside of the known laws of physics. Being outside of those laws, we could never detect it. If we observed a system spontaneously moving into a higher state of order, then we could never determine how that happened. We would need to start believing in miracles, and it would mark the demise of the scientific method. We would then assume that God will repair the damage we have caused to our environment. Oooops! Most people already do!

Patrick aka logicman (not verified) | 02/23/09 | 12:01 PM

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