The Onsager reciprocity relation and generalized efficiency of a thermal Brownian motor

Based on a general model of Brownian motors, the Onsagercoefficients and generalized efficiency of a thermal Brownian motorare calculated analytically. It is found that the Onsagerreciprocity relation holds and the Onsager coefficients are notaffected by the kinetic energy change due to the particle's motion.Only when the heat leak in the system is negligible can thedeterminant of the Onsager matrix vanish. Moreover, the influence ofthe main parameters characterizing the model on the generalizedefficiency of the Brownian motor is discussed in detail. Thecharacteristic curves of the generalized efficiency varying withthese parameters are presented, and the maximum generalizedefficiency and the corresponding optimum parameters are determined.The results obtained here are of general significance. They are usedto analyze the performance characteristics of the Brownian motorsoperating in the three interesting cases with zero heat leak,zero average drift velocity or a linear response relation, so thatsome important conclusions in current references are directlyincluded in some limit cases of the present paper.