7 An Unconventional Application
We will briefly discuss an application of quantum computing in quantum mechanics. Bennett’s analysis of reversibility [
12
,
13
] lead in 1982 to an unexpected reconciliation of Maxwell’s demon with the second law of thermodynamics. Maxwell’s Demon, a hypothetical intelligent entity capable of performing measurements on a thermodynamic system, was imagined by James Clerk Maxwell to “contradict" the second law of thermodynamics; see Maxwell [
94
], Leff and Rex [
86
]. Suppose that you have a box filled with a gas at some temperature. The average speed of the molecules depends on the temperature. Some of the molecules will be going faster than average and some will be going slower than average. Suppose that the box is divided by a partition into two parts, with both sides of the box filled with the gas at the same temperature. Maxwell imagined a molecule sized trapdoor in the partition and a demon poised at the door to observe molecules. The demon observes the molecules in the box as they approach the trapdoor, allowing fast ones to pass from left to right, and slow ones from right to left. After performing these operations the demon ends up with a box in which all the faster than average molecules are in the left side and all the slower than average ones are in the right side. So the box is hot on the left and cold on the right, and the expenditure of work is negligible, in apparent violation of the second law of thermodynamics.
Bennett built his solution on Szilard’s [
132
] subtle analysis of the Maxwell demon. Recall that Szilard invented the concept of a bit of information and associated the entropy 
ln
with the acquisition of one bit.
The resolution is that the demon must collect and store information about the molecules in the box (position and velocity of each molecule). A demon with a finite memory cannot continue to cool the gas indefinitely; eventually, information must be erased, and, as we now know, at exactly that point, we have to pay the “power bill". This argument has been extended to quantum physics and may be even experimentally testable, cf. Lloyd [
89
]; see also the discussion in Zurek [
145
].
The name “bit" was introduced only in 1946 by the statistician John Tukey.
