>>you can get 4-5 times as much heat out [...] > ..but why? Because you are literally pumping heat from outdoors to indoors. You are reducing the energy of th

>>you can get 4-5 times as much heat out [...] > ..but why? Because you are literally pumping heat from outdoors to indoors. You are reducing the energy of the outdoor air and increasing the energy of the indoor air. The electric energy spent is used to drive a motor that is pumping a fluid round in a loop. The pump is placed where you go from outdoors to indoors. Opposite the pump in the loop, you have a pressure reduction valve, and together these give you a higher fluid pressure on the indoor side, say 40 bar vs 20 bar. The trick is that this pressure difference means that the low pressure fluid is also cold, so it can be heated by the outside air, and the high pressure fluid is warm, so it can release heat to then indoor air. The thing about running hot water (e.g. district heating) is because you use heat that is literally free. E.g. if you have a waste incineration plant burning all the garbage, that's a lot of free heat. Or if you have a big data centre, lots of waste heat. Let's use it! In systems like the OP post, the water acts as both energy storage and a convenient way to distribute heat. No DC/AC inverter, etc.