Interesting idea. I wonder how much height difference you would need so that gravity gives you enough energy to power the regenerator at the bottom? The actual energy would come from ... the gravity field of the Earth?

The energy comes from the mass of oxygen that is released at the bottom and captured at the top.

But second law of thermo dynamics applies. If this works at all it is because you are capturing a little more of the energy that was put in at the top and would otherwise be lost. You stil need to put in external energy to keep this system running.

Shouldn't the needed energy increase the more the height difference? Seems it must be made up for in some other place too, or less waste heat at some stage.

The energy out increases by the height level as well.

If the process was 100% reversible, and friction free (probably a couple other loss factors I forgot about) it would be energy positive as the oxygen is making its way back up in the air is an external energy input. Of course in the real world both assumptions are wrong by more than enough that you can never get this to work.

Go ahead and stick a generator in between to capture some of the energy of the rust "flow" moving downhill for extra efficiency.

Haha, love that solution!