Does digital randomness require energy? I can't find anything related on Google. I hope this is the correct site to ask this question.

I have been thinking about Randomness. Basically, generating randomness using a Computer Program. It is impossible without a source of randomness. The entropy of the numbers is limited to what the source provide and its reliability.

So you can't get random numbers out of thin air. Does this mean that randomness requires 'energy'?

Sure energy is not enough to get real random numbers but is it a requirement for getting them?
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.