Eli5 – would it take more time/energy to boil a pint of frozen water or freeze a pint of boiling water?
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The total energy to _move_ is the same. Problem is cooling is much harder to do efficiently. To cool, you use electro-mechanical force to shove a gas between regions of high to low pressure (or tightly compressed to big volume; as the gas rapidly expands to fill the increased volume it draws thermal energy from the surroundings.) But the motors and pumps to do this are not perfectly efficient – some energy will be lost as waste heat from the mechanical bits, the motors/pumps etc. Meanwhile, if you use appropriate insulation you can extract nearly 100% of the input energy from an electric heating element. Thus to move the same amount of thermal energy either into or out of the water, its much more efficient to move it INTO the water with a heater than remove it using less efficient refrigeration.
And time is too variable – if you have a large enough heating element you can flash vaporize a pint of water instantly. Likewise if you had a super large chiller setup you could flash freeze a pint of water relatively quickly (not like, instantly, but within a minute or two.)
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