Differential temperature Carnot heat analysis shows that computing machines are thermodynamically irreversible

We perform a differential temperature Carnot analysis of the changes in energy and entropy (degrees of freedom) associated with an ideal classical computing machine. Assuming that Carnot's maximum efficiency law is as equally applicable to a computing machine as to a mechanical machine, we find that useful computation is necessarily dissipative and thermodynamically irreversible. In addition, we find that copying or cloning of information is as dissipative as the original process employed to create the information (through a computation) in the first place. We prove minimum heat dissipation kT ln 2 per output calculation bit, where T is the thermodynamic temperature of unavoidable by-product bits (i.e. not the output calculation bits) rather than a generally assumed 'surrounding environment' temperature. Overall, this places computers into the same category as conventional machines, obeying the second law of thermodynamics and always operating below 100% efficiency, such that a perpetual calculating machine cannot exist. © 2008 Elsevier B.V. All rights reserved.