What is Maxwell's Demon Paradox?

Updated on February 9, 2018
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Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly improve it.

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Physics is famous for its thought experiments. They are cheap and allow scientists to test out extreme conditions in physics to make sure that they work there also. One such experiment was Maxwell’s Demon, and since its mention by Maxwell in his Theory of Heat in 1871, it has provided countless individuals with enjoyment and physics with new insights into how we can resolve tricky situations.

The Demon

Another consequence of quantum mechanics, the set-up for Maxwell’s Demon goes like this. Imagine an insulated box filled with air molecules only. The box has two compartments that are separated by a sliding door whose function is to only allow I air molecule in/out at a time. The pressure differential between the two will end up being zero because the exchange of molecules via the door over time will allow the same number on each side based on random collisions, but said process could go on forever with no change in temperature to be had. That is because temperature is just a data metric indicating molecular motion and if we are allowing molecules to go back and forth in an enclosed system (because it’s insolated) then nothing should change (Al 64-5).

But what if we had a demon that could control that door? It would still allow only one molecule to pass at any time, but the demon could choose which ones go and which ones stay. What if it manipulated the scenario and only had fast molecules move to one side and slow ones to another? One side would be hot because of the faster moving objects while the opposite side would be colder because of the slower movement? We created a change in temperature where none was before, indicating that energy somehow increased and thus we have violated Thermodynamics’ Second Law, which states that entropy increases as time goes on (Al 65-7, Bennett 108).

Entropy!
Entropy! | Source

Entropy

Another way to phrase it is that a system of events naturally decays as time progresses. You don’t see a broken vase reassemble itself and rise back to the shelf it was on. That is because of entropy laws, and that is essentially what the demon is trying to do. By ordering the particles in a fast/slow section he is undoing what naturally happens and reversing entropy. And one is certainly allowed to do that, but at the cost of energy. That happens for example in the construction business (Al 68-9).

But that is a simplified version of what entropy is. On a quantum level, probability reigns supreme, and it is acceptable for something to reverse the entropy that it has gone through. It is possible for one side to have such a difference than the other. But as you get to a macroscopic scale, that probability rapidly approaches zero, so the Second Law of Thermodynamics is really the likely probability that we go from low entropy to high entropy over a span of time. And as we transition between states of entropy, energy is utilized. This can allow for an object’s entropy to decrease but the system’s entropy increases (Al 69-71, Bennet 110).

Now, let’s apply this to the demon and his box. We need to think about the system as well as the individual compartments and see what the entropy is doing. Yes, the entropy of each compartment seems to be going in reverse, but consider the following. At the molecular level, that door isn’t as solid as it appears to be and isn't really a collection of bounded molecules. That door only opens to allow a single of air through, but anytime one of them hits the door, an energy exchange is occurring. It has to occur, otherwise nothing would happen when the molecules collide and that violates many branches of physics. That minute energy transfer makes its way through the bounded molecules until it is transferred to the other side, where another colliding air molecule can then pick up that energy. So even if you got fast molecules on one side and slow on another, energy transference still happens. The box isn’t truly insulated then, and so the entropy does indeed increase (77-8).

Besides, if the fast/slow compartments were to exist, then not only would there be a difference in temperature but also in pressure, and eventually that door would be unable to open because said pressure would allow the fast molecules to escape to the other chamber. A slight vacuum generated by the forces of the particles would require they escape (Al 76, Bennett 108).

The Szilard Engine
The Szilard Engine | Source

New Horizons

So that is the end of the paradox right? Crack out the champagne? Not quite. Leo Szilard wrote a paper in 1929 entitled “On the Reduction of Entropy in a Thermodynamic System by the Interference of an Intelligent Being,” where he talked about a Szilard engine in the hopes of finding a physical mechanism where someone knowing controls particle flow and can violate the Second Law. It operates as follows:

Imagine we have a vacuum chamber with two pistons facing each other and a removable partition wall between them. Also consider a latch that holes the left piston and wall controls in it. One side measures the single particle in the chamber (causing it to fall into a state) and closes the door, closing off one half of the chamber. (Doesn’t the door moving use up energy? Szilard said it would be negligible to the dynamics of this problem). The piston in the empty chamber is released by the latch which was informed as to the identity of the empty chamber, allowing the piston to push up against the wall. This requires no work since the chamber is a vacuum. The wall is removed. The particle hits the piston which is now exposed because of the wall being removed, forcing it back to its starting position. The particle does lose heat because of the collision, but is replenished from the environment. The piston resumes its normal position and the latch is secured, lowering the wall. The cycle then repeats indefinitely and the net loss of heat from the environment violates entropy…or does it? (Bennett 112-3)

If we have someone who knowingly controls the flow of the molecule between two compartments like our original setup but there it turns out that the energy required to move the fast and slow onto each side is the same as if it were at random. This isn’t the case here because we now have a single particle. So it isn’t the solution we were looking for because the energy condition was already present with the non-demon setup. Sometihng else is amiss (Al 78-80, Bennett 112-3).

That something is information. The actual changing of neural pathways in the demon is a reconfiguration of matter and therefore energy. Therefore, the system as a whole with the demon and the box does experience a decrease in entropy, so all together the Second Law of Thermodynamics is indeed safe. Rolf Landauer proved this in the 1960’s when he looked at computer programming regarding data processing. To make a bit of data requires matter rearrangement. It move data from one place to the other takes up 2^n spaces, where n is the number of bits we have. This is because of the movement of bits and the places they hold as they are copied. Now, what if we cleared all the data? Now we have just one state, all zeros, but what happened to the matter? Heat happened! Entropy increased even as data was cleared. This is analogous to the mind processing data. For the demon to change his thoughts from state to state requires entropy. It has to happen. With regard to the Szilard engine, the latch having its memory cleared would too require an increase in entropy by the same measure. Folks, entropy is okay (Al 80-1, Bennett 116).

And physicist proved it when they built an electron version of the engine. In this set-up, the particle can move back and forth between the divided partitions via quantum tunneling. But when a sensor applies a voltage, the charge will be trapped in a section and information will be gained. But that voltage requires heat, proving that the demon does indeed expend energy and thus maintains the amazing Second Law of Thermodynamics (Timmer).

Works Cited

Al-Khalili, Jim. Paradox: The Nine Greatest Enigmas in Physics. Broadway Paperbacks, New York, 2012: 64-81. Print.

Bennett, Charles H. “Demons, Engines, and the Second Law.” Scientific American 1987: 108, 110, 112-3, 116. Print.

Timmer, John. “Researchers Create a Maxwell’s Demon with a Single Electron.” Arstechnica.com. Conte Nast, 10 Sept. 2014. Web. 20 Sept. 2017.

© 2018 Leonard Kelley

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