Maxwell’s demon is an interesting thought experiment on the 2nd law of thermodynamics. I have thought about this experiment for some time, and I think I have found a rebuttal.
In simple terms, this thought experiment suggests a way (using a tiny trapdoor between the A side and the B side of a gas container) to separate hot and cold gases without doing any work. The idea is that Maxwell’s demon opens the trapdoor when a fast moving molecule from A side approaches the trapdoor, thus allowing it to “leak” to B’s side, and similarly allowing for slow moving molecules from B side to leak to A side. If this way was theoretically possible, then we would be able to create more order, thus, in principle violating 2nd law of thermodynamics. Various criticisms have been given in an attempt to uphold our believe that 2nd law of thermodynamics is true (so, it is in fact a law).
Firstly, I must say that I do not agree with the rebuttals by Szilard, Brillouin and Charles Bennett, because their criticism is mostly on the energy that would be required to measure the speed of molecules and to operate the trapdoor. However, this is an assumption, not a fact. This assumption can be considered a fact, if we do choose to believe in many existing laws of physics, of which, second law of thermodynamis is one. Thus, this entire logic is circular.
My logic is different, and does not depend upon the assumption that energy is required to measure the speed of molecules. We consider two cases.
Case I: Trapdoor has a certain mass. If the trapdoor has mass, then to open or close it, we must expend some energy. thus the entire setup is not isolated. In that case, second law of thermodynamics is not violated at all.
Case II: Trapdoor is massless. If the trapdoor is massless, then we are not spending any energy in opening or closing it. However, if it is massless, then when a fast moving molecule hits it from the B side, some energy must be expended to keep the trapdoor from opening to A side. So, in this case second law of TD is not violated.
So, in all cases, we can see that Maxwell’s demon can be theoretically refuted.