There have been some recent papers on harvesting electrical energy from air humidity using nanoengineered materials:
"Power generation from ambient humidity using protein nanowires" in Nature
"Generic Air-Gen Effect in Nanoporous Materials for Sustainable Energy Harvesting from Air Humidity" in Advanced Materiels
These articles are paywalled, but have some popular science articles, e.g.
"Nanopores are the secret to making electricity from thin air"
"Scientists Working to Generate Electricity From Thin Air Make Breakthrough
and at least one patent application.
Can the theoretical maximum energy harvesting rate be estimated per unit area of the material, and if yes, what is it? I guess this should be calculable from the air humidity, temperature, and pressure, and the latent heat of condensation of water, possibly with some assumptions about air flow over the surfaces. (I assume the energy is coming from condensation which means the device also produces possibly useful liquid water, but I don't immediately see this mentioned in the articles.)
The EU has provided €3M in funding to the CATCHER project for developing humidity-to-electricity conversion with an objective of a power density of ~36 mW/g or 15 - 20 mW/cm$^2$, but I don't know if these are theoretical limits or just practical goals.
Clarification Update
Just to be clear, I am asking if there is some bound on the energy harvesting rate similar to how the solar constant sets an upper bound on solar energy, how Carnot's Theorem limits thermal generation (e.g. as discussed in this question about thermoelectric generation), or how wind turbine power is constrained by the Betz Limit. This question is not about how practical the technology is or whether it could compete against wind, hydro, or other power technologies that directly or indirectly also harvest energy from the atmosphere.
