Optimal efficiency condition and current reversals in forced underdamped ratchets

The condition of optimal efficiency in the energy transformation of a massive Brownian particle, moving in an asymmetric potential and subject to an external driving force, is studied by direct simulation of the stochastic differential equations. We analyze the behavior of the stationary averaged current and, at the same time, the energetic efficiency is evaluated. We found that the current exhibits several reversals when plotted as a function of the mass, and that it can be optimized at a particular value of the temperature. The condition to achieve an optimal efficiency is found, relating the mass, temperature and friction to the properties of the ratchet potential.