On how nanomechanical systems can minimize dissipation

Information processing machines at the nanoscales are unavoidably affected by thermal fluctuations. Efficient design requires understanding how nanomachines can operate at minimal energy dissipation. In this letter we focus on mechanical systems controlled by smoothly varying potential forces. We show that optimal control equations come about in a natural way if the energy cost to manipulate the potential is taken into account. When such cost becomes negligible, the optimal control strategy can be constructed by transparent geometrical methods and recovers the solution of optimal mass transport equations in the overdamped limit. Our equations are equivalent to hierarchies of kinetic equations of a form well-known in the theory of dilute gases. From our results, optimal strategies for energy efficient nanosystems may be devised