The problem is, I don’t believe it’s at a minute-by-minute level of granularity. If you’re working several hours a day at tipped minimum, and the rest making well above minimum after tips, repeat the above daily and average at minimum wage for the pay period… That’s good enough.
It takes less energy to move heat than it does to produce it. A heat pump basically runs an air conditioner backwards, so rather than moving heat from inside a structure to outside, it moves heat from outside to in. With the right units, this works even in cold weather for the same reason a freezer gets warm on the outside - it’s moving heat from inside the (freezing) unit out.
Geothermal energy takes this concept a step further by putting the outside unit underground. Underground temperatures are more stable and moderate, so it’s easier (more efficient) to expel/collect heat, but also much more involved to install.