I have a bucket that weighs 0.2 kg and contains 1 kg of boiling water. The thermal energy of the water in my bucket is mass * heat capacity of water * temperature in Kelvin = 1 kg * 4.2159 J/g/K * 373.15 K =
1.573 MJ. Now I lift this bucket with boiling water 1 meter straight up, the labour I need to do this is mass * gravitational field strength * distance = 1.2 kg * 9.81 N/kg * 1 m =
11.8 J. I moved 13330000% more energy than I used energy to move it, but I did not create any energy.
This example demonstrates the difference between moving energy and using energy. This example is not a heat pump though, since there is no transfer of thermal energy between masses, the mass itself is moved instead. The "efficiency" of a heat pump is expressed in how much energy it moves between masses compared to how much energy it uses to do so. Note that using energy just means transforming energy from one form (e.g. electricity) to another (e.g. heat), not making energy disappear.
My own house is not heated by heat pumps but by a central heating system, where various gas burners at the top floor of the flat heat water and pump it through mostly unisolated metal tubes to radiators inside the apartments. I cannot answer whether I have "free electricity" in winter, because while gas is cheaper than electricity in my country, I don't know how efficient the central heating system is (definitely lower than 100% when counting only the heat that ends up in my home) nor what gas-price the landlord charges me per kWh of heat brought to my home. There is no singular answer to the "free electricity"-question because it depends on the specific prices and efficiencies of the various heating systems available in a region. Comparing the price-ratio and efficiency-ratio between GPU-heating and other heating, will determine whether you save or spend more money when mining compared to other heating. Even when spending more, since you also get Bitcoin rewards, you may still come out with profit.
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