Maxwell's Demon

You should call it entropy, for two reasons. In the first place, your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one knows what entropy really is, so in a debate you will always have the advantage .....................

John von Neumann to Claude Shannon, as quoted by Sean Carroll in From Eternity to Here.

Luboš is busily increasing the entropy of the blogosphere, and his target again is Sean Carroll. At the center of the dispute is Maxwell's Demon. Maxwell cooked the little guy up to test some ideas of statistical mechanics. Imagine a box containing a gas of molecules, with a small hole leading to an empty box and a little guy standing at the hole with a little door he can shut. His job is to open the door when he sees an especially fast molecule coming along and close it for the slow molecules (the other way around would work similarly).

Sean's (imaginary) crime was to (truthfully) claim that information could be used to extract energy from a similar system. Luboš managed to convince himself that this was (a) violating the second law of thermodynamics and (b) claiming that information and energy are the same thing. I don't think that either of these is remotely close to what Sean was saying, and that Luboš has once again allowed his prejudices to overcome his rationality.

That said, Lumo's post is very interesting in it's own regard, mainly for its links to some other interesting papers, but I will send you to him for them.

Back to Maxwell's demon. Can he really do that? Work some kind of little door to cool one box while warming the other? Sure he can. He is doing the work of a kind of refrigerator. Lumo the particle physicist is doubtless familiar with the concept of stochastic cooling used in large partice accelerators. It's a sort of Maxwell's Demon used to cool bunches of particles circulating in the storage rings.

So does this violate the second law? Duh, no. Like any other refrigerator, Maxwell's demon extracts entropy from one part of the universe but dumps it and more into some other part. The system Sean describes, Maxwell's Demon, and the stochastic cooling mechanism all make use of information about details of the system to selectively extract energy from a subsystem of the world.

Question for the student: How about ordinary refrigerators, like the ones in most of our kitchens? Is there any sense in which they do something similar? Use subsystem information to extract entropy, I mean.