Yeah, as I mentioned in a sibling comment, erasure of data is an irreversible process that (because of thermodynamics) will always create heat (even of everythi

Yeah, as I mentioned in a sibling comment, erasure of data is an irreversible process that (because of thermodynamics) will always create heat (even of everything is a efficient as the laws of the universe permit). That heat is energy and it has mass. It is actually straightforward to prove it would have the same mass as the initial information pattern. A string of zeroes and a random string do have different amount of entropy, so transforming between them requires energy.