Rectification efficiency of a Brownian motor

Abstract

The energy balance of a Brownian motor is discussed based on a Langevin equation without the overdamped approximation. Energetics of the system suggests that the frictional dissipation energy associated with the unidirectional movement should be counted as a part of the useful energy for the rectification process of a Brownian motor. This leads to a new definition of the efficiency, which is applicable, contrary to the conventional one, even if the external load is absent. For the so-called flashing ratchet model, we numerically solve the Langevin equation for various situations and discuss both the temperature and the friction strength dependence of the rectification efficiency and the role of the duty ratio.