热驱动布朗马达性能的非平衡态热力学分析

Nonequilibrium thermodynamic analysis on performance of an thermally driven Brownian motor

基于一个普遍的布朗马达模型,建立了一个等效的循环系统,运用非平衡态热力学理论计算了系统的昂色格系数和最大输出功率时的效率。发现模型的昂色格系数满足倒易关系,对于现实系统的不可逆因素同样会影响模型的昂色格系数。仅当热漏和粒子动能改变部分可以忽略时,昂色格系数行列式等于零。同时还发现在非平衡态热力学框架下,对于不可逆热布朗马达的输出功率和效率可以表述成和不可逆卡诺热机相同的形式,因此所得的结果更具有普遍意义。此外,这些结论还可以用来分析一类热驱动布朗马达的性能特性。

Based on the general model of thermally driven Brownian motors, an equivalent cycle system is established and the Onsager coefficients and the efficiency at the maximum power output of the system are analytically calculated from nonequilibrium thermodynamics. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are affected by the main irreversibilities existing in practical systems. Only when the heat leak and the kinetic energy change of the particle in the system are negligible, can the determinant of the Onsager matrix vanish. It is also found that in the frame of nonequilibrium thermodynamics, the power output and efficiency of an irreversible Brownian motor can be expressed to be the same form as those of an irreversible Carnot heat engine, so the results obtained here are of general significance. Moreover, these results are used to analyze the performance characteristics of a class of thermally driven Brownian motors.