Comment by PaulHoule
Notably the physical limit is
https://en.wikipedia.org/wiki/Landauer%27s_principle
it doesn't necessarily take any energy at all to process information, but it does take roughly kT work of energy to erase a bit of information. It's related to
https://en.wikipedia.org/wiki/Maxwell%27s_demon
as, to complete cycles, the demon has to clear its memory.
Does it not take energy to process information? Can any computable function be computed with arbitrarily low energy input/entropy increase?