  We consider a molecular machine described as a Brownian particle diffusing in
a tilted periodic potential. We evaluate the absorbed and released power of the
machine as a function of the applied molecular and chemical forces, by using
the fact that the times for completing a cycle in the forward and the backward
direction have the same distribution, and that the ratio of the corresponding
splitting probabilities can be simply expressed as a function of the applied
force. We explicitly evaluate the efficiency at maximum power for a simple
sawtooth potential. We also obtain the efficiency at maximum power for a broad
class of 2-D models of a Brownian machine and find that loosely coupled
machines operate with a smaller efficiency at maximum power than their strongly
coupled counterparts.
