> And no, this is not something permitted by the second law of thermodynamics.

If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations—then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation—well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

While I generally agree that it sounds dubious, this argument depends on whether the entropy of the liquid in the pore is lower than the entropy of the vapor in the air in the pore. I could see a highly hydrophilic capillary restricting a vapor enough to where it has better entropy in a liquid state.

If that's true we just need to balance energy, which the cooler does.

Practically it just means that the energy to form the droplets is coming from somewhere else, just not via cooling the surface below the dew point. For instance, you could imagine something like squeezing a material that undergoes capillary condensation to get the water out, since you'd pay the requisite energy cost via mechanical work.