At a recent workshop Luca Peliti mentioned Smoluchowski’s proposed realization of an antisymmetric “Maxwell demon”. Right afterwards with some of the participants we started discussing how the system would behave and decided to finally take a little bet (not much, a bottle of good quality Rum). It turned out that the betting process itself is an interesting sociological experiment in itself, as the specification of the conditions, of the meaning of concepts, and of the procedure by which the bet would be claimed to be won are far from settled. So here this post, in the hope that it might draw more discussion and to an agreement.
So here the situation. There’s a gas in a box, with a wall in between and a small opening with a door. The door opens and closes asymmetrically only on one side, and there’s a coiled spring exerting a restoring force to close it. The spring is embedded in wall and door, so that it does not interact with the gas. The system is overall isolated. We assume that before time t=0 the door is kept open by some string, and that the gas has been prepared at equilibrium with a well-defined notion of temperature (e.g. by putting it in contact with a reservoir that was then removed some time in the past, that is the same on both sides of the box. At time t=0 the string is cut with minimal effort. As well known in all these cases, the door can occasionally be opened by molecules hitting on it from one side. Hence there might or might not be a displacement of particles. We assume there is no interaction between particles nor dissipation due to interaction with the walls. The question is whether the temperature of the gas will be the same on the two sects after a sufficiently long time has passed.
The kind of argument I’m interested in is one where the details of the system do not matter so much, the number of particles, the mass of the door, the string constant etc. I have many personal reasons why I like this problem and I have my own opinion on it.