[measurablefunc]

That's clever accounting but your overall system (house + outside + plant + fuel) is still less than 100% efficient. That's basic physics/thermodynamics.

Heat pumps are basically taking advantage of solar + geothermal radiation that ends up in the ground & air but once you account for the solar + geo radiation then it becomes obvious that all a heat pump is doing is accelerating the production of entropy. You're either normalizing the delta between inside & outside or increasing it but in both cases the overall entropy of the system goes up. Whereas your accounting seems to suggest you somehow get more energy than what was available which is obviously unphysical.

[_aavaa_]

Sure.

But my accounting was always about the energy that we as humans need to supply. This discussion was originally about how talking about the energy transition in terms of primary energy is inherently misleading.

A heat pump does not magically create the difference between work input and heat output, it pulls it from second source. But that source is free. All we have to provide is the work.

Replacing a gas burner with a heat pump does not require us to replace 1 J of chemical potential energy with 1 J of electricity, instead replace it with 0.33 J of electricity (or even less).