  Efficiency of a Brownian particle moving along the axis of a
three-dimensional asymmetric periodic channel is investigated in the presence
of a symmetric unbiased force and a load. Reduction of the spatial
dimensionality from two or three physical dimensions to an effective
one-dimensional system entails the appearance of entropic barriers and an
effective diffusion coefficient. The energetics in the presence of entropic
barriers exhibits peculiar behavior which is different from that occurring
through energy barriers. We found that even on the quasistatic limit there is a
regime where the efficiency can be a peaked function of temperature, which
indicates that thermal noise can facilitate energy transformation, contrary to
the case of energy barriers. The appearance of entropic barriers may induce
optimized efficiency at a finite temperature.
