This maybe?

recharge via Brownian motion is a second-law perpetual motion machine

Is a thermopile second order perpetual motion? No they generate output voltage due to a temperature difference.

I respectfully disagree, that Brownian motion is perpetual motion. Recharge via Brownian motion is a real observable phenomenon the input energy is heat from the environment. Asymmetric electrodes can be tuned to have pores suited to certain ions. They demonstrate an electrolytic double layer by intercalating the ions asymetrically in the electrodes.

As, I said before the effect is so minuscule and the lack of energy density makes the cell useless besides being a trinket.  If it could be made better it could be used to recycle waste heat from a steam power plant.

Ah, an temp difference, then there is no problem. 

Brownian motion at constant temp cannot work.

Yes I will build one to demonstrate using asymmetric carbons, I really don't have a clue how or why it works, I highly doubt there is a daemon involved:)

Another perpetual motion machine?

Well there is such a thing as a Karpen cell that can recharge due to brownian motion. The recharge rate is so low and the energy density miniscule that it doesn't make any sense.

Edit: But if he can improve on it I am all eyes.