[DoctorOetker]

a counter current heat exchanger might be more reliable than a refrigerant heat pump and more efficient than peltier heat pumps, but yes in theory you can quasistatically move the water out for almost no energy (only the adsorption / mixing energies). And peltiers can be much more efficient at tiny temperature gradients, so a theoretical frictionless positive displacement pump, and a heat pipe between the condensing compartment and the evaporatig compartment (so keeping the 2 compartments at ambient temperature (so no heat losses).

Compressing humid air releases heat which marginally increases the temperature of the condensing compartment, and marginally cools the evaporating compartment with the wet clothes; thus the heat pipe will quickly equilibrate the 2 compartments.