Maxwell's Demon

Fallen Seraph

Is there any proof (mathematical, not empirical :P) that a valve which selectively allows through fast molcules, but not slow molecules cannot violate the second law of thermodynamics?

Son Goku

Yes, there is. It's in Maxwell's collected works. I could easily get my hands on it if you want to see it (I'd scan it) or do you just want to know it exists?

Fallen Seraph

Oh I would indeed like to see it. If you could scan it it'd be great, but if you want to save yourself the trouble you can always just point me to the part of his works that has it, and I'm sure I can get it in the library. Thanks a lot.

Professor_Fink

Hi F.S.,

Basically it is impossible to build such a device which does not use energy. The problem is often brought up in information theory. Basically the valve has to process information. It can only have a finite storage capacity as it is a finite device. After it measures a particle to decide whether or not to let it through it must then erase the measurement result to make room for the next one. Unfortunately there is a minimum energy cost associated with erasing information, preventing the machine from producing a net gain in energy.

The Chapter 3 of 'Quantum Computation and Quantum Information' by Michael Nielsen and Isaac Chuang covers it in some detail. See page 162.

Fallen Seraph

Thanks for the info, but I know that things get sticky if info-processing is involved. Reading back on it, my first post is a bit vague; I was actually thinking of a sort of trap-door setup; where fast molecules have enough energy to make it through, and slow ones don't. I've no doubt that it doesn't work, I'd just be interested to see what a proof of it looks like.

Thanks for the reference though, I shall be looking that up.

Professor_Fink

Fallen Seraph wrote:

Thanks for the info, but I know that things get sticky if info-processing is involved. Reading back on it, my first post is a bit vague; I was actually thinking of a sort of trap-door setup; where fast molecules have enough energy to make it through, and slow ones don't. I've no doubt that it doesn't work, I'd just be interested to see what a proof of it looks like.

Thanks for the reference though, I shall be looking that up.

Well in the case you mention it won't work because eventually you'll get molecules going the same way. i.e. when 1 goes in, 3 go out. It's exactly the same argument why Brownian rachets don't work.