Can i exploit johnson noise to violate the second law?

[parsec]

Thermal noise known as “Johnson noise” or “Nyquist noise” is well known and characterized. This noise is a result of thermal agitation of charge carriers inside a conductor. Its power spectral density is given by:

v^2=4kTRwhere kB is Boltzmann's constant in joules per kelvin, T is the resistor's absolute temperature in kelvins, and R is the resistor value in ohms.

Imagine a resistor in an adiabatic enclosure (one incapable of heat transfer) connected to a lossless diode. The wires leave the enclosure through sealed ports to power a circuit. Shouldn’t the rectification of this random fluctuation in the voltage across the resistor create a net positive voltage and hence allow us to violate the second law of thermodynamics (creating free energy)?

I once asked a physics professor this question and he excitedly gave me a rushed explanation of why this wouldn’t work. It involved Brownian motion and he quickly digressed into a tangent about proving the continuity between classical (Rayleigh Jeans) and quantum blackbody theory. It involved some esoteric thought experiment where he defiled my adiabatic enclosure with a big parabolic dish. I wasn’t impressed.

edit: I just realized the parallels between this hypothetical and Maxwell's demon, which seems to be still up for debate.

 

[Cthugha]

It is not that easy. What you present here is a version of Smoluchowski's Trapdoor, I think.

The problem is your diode. A diode is not a perfect binary switch. It is subject to thermal noise as well. Therefore you will only notice some net electron movement, if there is a temperature gradient between the diode and your conductor. This thing will work similar to a thermocouple.
Have a look at the Seebeck-effect. It is very similar.