I would include the energy needed to maintain trust in other currencies including efforts to prevent counterfeits, which I might argue includes some portion of a nation's militaristic might. Trust is an even more ambiguous, yet crucial aspect of maintaining a currency's value, tied up in the "order" or predictability of the society using the currency, which involves various legal systems and at the most basic level, relationships between its peoples.
It takes a relatively minuscule amount of energy to maintain a database of numbers associated with certain people and entities, but quite a significant amount to make it mean something.