  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
