Logical Dissipation of Automata Implements - Dissipation of Computation
  As revealed by discussions of principle on energy dissipation by computers, logic imposes constraints on physical systems designed for a logical function. We define a notion of logical dissipation for a finite automaton. We discuss the constraints associated with physical implementation of automata and exhibit the role played by modularity for testability. As a result, practical computers, which are necessarily modular, dissipate proportionally to computation time. 
Philippe Matherat (Ecole Nationale Supe'rieure des   Te'le'communications) and Marc-Thierry Jaekel (Laboratoire de Physique ...