I would like to understand where the waste heat is generated in the Maxwell's demon problem. To this end I've come up with the simplest scenario I can think of. If my scenario is workable I am hoping someone will be kind enough to apply the right math to it to show what is going on and why it does not work to provide a "free lunch."
My scenario is as follows:
Take a 1 dimensional container of length l. Start with an evenly distributed population of particles; slow red ones and fast blue ones, traveling at +v or -v, and +2v or -2v respectively.
The demon sits at the boundary at l/2.
He lets slow red particles at +v and fast blue particles at -2v through and keeps the opening between the two halves of the container closed otherwise.
The idea of using a one dimensional container is to keep the math as simple as possible. In order for this to work the particles have to be able to go right through one another without interacting.
I am imagining that if one can work out what happens in this simplest case then it should be possible to extend the scenario to a 2-dimensional container in which the line forming the barrier between the two halves of the container is made up of discrete copies of the Maxwell's Demon in my 1-dimensional scenario.