Does digital randomness require energy?
Everything that happens on computers requires some energy. This includes the very act of looking up random values from any source.

There is a mythical beast called reversible computing which is basically computing without using up energy. It's unclear whether it can exist at all; but laws of physics (as we currently understand them) imply that reversible computing must also be logically reversible. This is known as Landauer's principle: if some information is erased in a process, then entropy (the physical notion) rises and this requires usage of some energy. Thus, computing a hash function necessarily requires some energy.

Note that this notion is about the conservation of information: it's not obtaining randomness that matters; it's about what you do with it.