Transport enhancement and efficiency optimization in two heat reservoir ratchets

We study a Brownian motor moving in a sawtooth potential in the presence of an external driving force and two heat reservoirs. Based on the corresponding Fokker--Planck equation, the analytical expressions of the current and efficiency in the quasi-steady-state limit are obtained. The effects of temperature difference and the amplitude of the external driving force on the current and efficiency are discussed, respectively. The following is our findings. (i) The current increases with both \delta and A. In other words, \delta and A enhance the transport of the Brownian motor. (ii) The competition between the temperature difference and the amplitude of the external driving force can lead to efficiency optimization. The efficiency is a peaked function of temperature, i.e., \delta>0 and a lower amplitude value of the external driving force is necessary for efficiency optimization. (iii) The efficiency increases with \delta, and decreases with A. \delta and A play opposite roles with respect to the efficiency, which indicates that δ enhances the efficiency of energy transformation while A weakens it.