That's the thing: it doesn't! (i.e. Processing data doesn't need energy - more correctly "work") In the limit, you can process information adiabatically.(*) i

That's the thing: it doesn't! (i.e. Processing data doesn't need energy - more correctly "work") In the limit, you can process information adiabatically.(*) i.e. you can perform a computation without heat exchange, and you can perform computations reversibly. Maxwell's demon as a thought experiment is actually quite a deep and subtle probe into the boundary between information and thermodynamics. What you CAN'T do adiabatically or reversibly is clear or set bits and throw away their initial state. In theory you could make a classical mechanical turing machine that could perform a computation for an arbitrarily small amount of work, but to prepare a blank tape for it (or to configure a tape into a known configuration) will take a certain minimal expenditure of work. * Ignoring Quantum Physics for now The Wikipedia page for Reversible Computing might be a place to start reading if you're interested in following up.