There's a reasonable amount of history behind the demon. When Maxwell first conceived of it, he realised that it could violate the second law of thermodynamics but neither he nor his comtemporaries attached much importance to it because of the the extremely implausible nature of the demon. Szillard came up with his explanation to save the second law in 1929 when he showed that in discriminating between a hot and cold molecule, the demon would end up increasing entropy.
There's another way to look at this and that is that erasure of information is necessarily a dissipative process which increases entropy. Since the demon must have a finite memory capacity(in which he stores whether a molecule is hot or cold) at some point of time, he would run out of memory cells and then he would need to reuse some of them. This is what would increase entropy.
This idea probably sounds strange but is pretty easy to understand. Lets say we have a box with a molecule inside it. If the molecule is on the right side we take that to mean 1 and if the molecule is on the left we take that to mean 0. Thus the box forms a memory unit. Now to erase the information in the box, we would need to compress the gas(???) till the molecule was definitely on one side. Then whatever information the box contained previously would be lost. To do this clearly involves a change in entropy of kTln(2).
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This has important consequences for Quantum Computing. In normal computing most gates involve the loss of one bit. For example an AND gate takes in two bits, and gives out one bit and this involves erasure of information. A quantum computer must be reversible(because irreversible processes invole interaction with classical objects(measurements) and this would destroy coherence). Thus a Quantum Computer cannot function this way and must use reversible gates. All classical computation may be performed reversibly by replacing NAND gates with what are called Toffoli gates. Quantum computation involves a more general gate however and the universal reversible quantum gate is the Deutsch gate.
Please msg me if some of the arguments in this node are unclear.
A footnote: On the suggestion of
CapnTrippy, here's this conclusion.
Maxwell's demon and Quantum Computation are two seperate things but the fact that information is physical and deletion increases entropy can be used to explain Maxwell's demon and has important consequences for Quantum Computing. That is the common link and thats why I put both things together.