This does not apply to pv cells or heat pumps.
The best definition of FE efficiency, in my view, is Patrick's:
Energy out --------------------- = OU rate Energy YOU put in
I agree, but only within a framework that must absolutely be defined and specified: the closed system. Another important notion to specify is the form of recovered energy. If it's heat, it's a degraded form not really "useful" energy. If your closed system is the PV cells, the electrical energy is free, the entropy decreases locally. If your closed system is the solar system, the energy is not free, neither for the PV cells nor for the heat pump, because its entropy increases. If your closed system is the heat pump alone, or the earth + the heat pump, the energy is not free either. It is true that you get back more energy than you put into it, but this energy is degraded energy (heat). This energy does not make it possible to close the system because the conversion thermal energy/electric energy has a weak theoretical efficiency, and in practice even weaker. Therefore, it is always necessary to supply the heat pump with energy that is not free, the entropy increases. Of course, I agree that what we are interested in is a local useful energy, so a decrease of the local entropy, no matter if we increase the one of the rest of the universe. If in this sense the electric energy of a solar panel is indeed free, that of a heat pump is not. To loop a heat pump would be to carry out a demon of Maxwell. A Maxwell's demon has never been proved not to exist in general, but the attempts I have seen so far only concern really low energy levels, leaving serious doubts about possible experimental artifacts.
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"Open your mind, but not like a trash bin"
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