中国物理B ›› 2009, Vol. 18 ›› Issue (8): 3279-3286.doi: 10.1088/1674-1056/18/8/031

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

张悦1, 高天附2, 陈金灿2   

  1. (1)College of Information Science and Engineering, Huaqiao University, Quanzhou 362021, China; (2)Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, China
  • 收稿日期:2008-12-23 修回日期:2009-02-07 出版日期:2009-08-20 发布日期:2009-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10575084).

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

Gao Tian-Fu(高天附)a), Zhang Yue(张悦)b), and Chen Jin-Can(陈金灿)a)†   

  1. a Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, China; b College of Information Science and Engineering, Huaqiao University, Quanzhou 362021, China
  • Received:2008-12-23 Revised:2009-02-07 Online:2009-08-20 Published:2009-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10575084).

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摘要： Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle's motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper.

Abstract: Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle's motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper.

Key words: Brownian motor, Onsager coefficient, generalized efficiency, performance characteristic

中图分类号:  (Brownian motion)

  • 05.40.Jc
02.10.Yn (Matrix theory) 05.70.-a (Thermodynamics)