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研究了单势垒锯齿势中，布朗粒子在外力和空间周期温度场作用下构成的布朗热机的热力学性能. 考虑布朗粒子动能变化以及高、低温库之间热漏引起的热流. 用Smoluchowski 方程描述粒子在黏性介质中的动力学特性，推导出高、低温库的热流以及热机功率和效率的解析表达式. 通过数值计算分析势垒高度、外力和温库边界对热机性能的影响. 研究表明：由于动能变化和热漏引起的不可逆热流的存在，布朗热机为不可逆热机，热机的功率效率特性为一闭合的关系曲线；势垒边界与温库边界重合时，热机的功率达到最大值；通过改变温库边界的位置，可以在一定范围内提高热机的效率，但同时减小了热机的输出功率.In this paper we study the thermodynamic performance of a Brownian heat engine, which is driven by temperature difference. Brownian particles move in a periodic single-barrier sawtooth potential under the action of an external load force, and contact an alternating hot and cold reservoir. The kinetic energy change of the Brownian particles and the heat leak between hot and cold reservoir are considered simultaneously. The dynamics of the Brownian particle is governed by the Smoluchowski equation. The expressions for heat flow, power output and efficiency are derived analytically. The influences of the height of barrier, the external load force and the heat reservoir boundary on efficiency and power output are discussed by numerical calculation. It is shown that the Brownian heat engine is irreversible when the irreversible heat flow caused by the kinetic energy change and the heat leak exist. The curve of the power output versus the efficiency is a loop-shaped one. When the barrier boundary coincides with the heat reservoir boundary, the heat engine has a maximum power output. The efficiency of the heat engine is enhanced, but the power output is reduced when the heat reservoir boundary is changed.
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Keywords:
- Brownian heat engine /
- heat leak /
- thermodynamic performance /
- irreversibility
[1] Hanggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 387
[2] Astumian R D, Bier M 1994 Phys. Rev. Lett. 72 1766
[3] Parrondo J M R, Blanco J M, Cao F J 1998 Europhys. Lett. 43 248
[4] Ambaye H, Kehr K W 1999 Physica A 267 111
[5] Feynman R P, Leighton R B, Sands M 1963 The Feynman Lectures on Physics. (Vol. I) (Boston: Addison-Wesley) Reading 46.1
[6] Bttiker M 1987 Z. Phys. B 68 161
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[9] van den Broeck C, Kawai R 2006 Phys. Rev. Lett. 96 210601
[10] Li N, Zhan F, Hanggi P, Li B 2009 Phys. Rev. E 80 011125
[11] Li N, Hanggi P, Li B 2008 Europhys. Lett. 84 40009
[12] Asfaw M, Bekele M 2004 Eur. Phys. J. B 38 457
[13] Asfaw M, Bekele M 2005 Phys. Rev. E 72 056109
[14] Asfaw M, Bekele M 2007 Physica A 384 346
[15] Derényi I, Astumian R D 1999 Phys. Rev. E 59 R6219
[16] Zhang Y P, He J Z, He X 2010 Commun. Theor. Phys. 54 857
[17] Zhang Y P, He J Z, Ouyang H 2010 Phys. Scr. 82 055005
[18] Zhang Y P, He J Z 2010 Chin. Phys. Lett. 27 090502
[19] Luo X G, Liu N, He J Z 2013 Phys. Rev. E 87 022139
[20] Hondou T, Sekimoto K 2000 Phys. Rev. E 62 6021
[21] Ai B Q, Xie H Z, Wen D H 2005 Eur. Phys. J. B 48 101
[22] Ai B Q, Wang L Q, Liu L G 2006 Phys. Lett. A 352 286
[23] Ai B Q, Wang X J, Liu G T 2003 Phys. Rev. E 68 061105
[24] Zhang Y, Lin B H, Chen J C 2006 Eur. Phys. J. B 53 481
[25] Lin B H, Chen J C 2009 J. Phys. A: Math. Theor. 42 075006
[26] Ding Z M, Chen L G, Sun F R 2010 Braz. J. Phys. 40 141
[27] Ding Z M, Chen L G, Sun F R 2010 Sci. China G: Phys. Mech. Astron. 40 16 (in Chiese) [丁泽民, 陈林根, 孙丰瑞 2010 中国科学 G辑: 物理学 力学 天文学 40 16]
[28] Asfaw M 2008 Eur. Phys. J. B 65 109
[29] Asfaw M 2014 Phys. Rev. E 89 012143
[30] Cheng H T, He J Z, Xiao Y L 2012 Acta Phys. Sin. 61 010502 (in Chinese) [程海涛, 何济洲, 肖宇玲 2012 61 010502]
[31] Sancho J M, Miguel M S, Drr D 1982 J. Stat. Phys. 28 291
[32] Gao T F, Zhang Y, Chen J C 2009 Chin. Phys. B 18 3279
[33] Gordon J M, Huleihil M 1992 J. Appl. Phys. 72 829
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[1] Hanggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 387
[2] Astumian R D, Bier M 1994 Phys. Rev. Lett. 72 1766
[3] Parrondo J M R, Blanco J M, Cao F J 1998 Europhys. Lett. 43 248
[4] Ambaye H, Kehr K W 1999 Physica A 267 111
[5] Feynman R P, Leighton R B, Sands M 1963 The Feynman Lectures on Physics. (Vol. I) (Boston: Addison-Wesley) Reading 46.1
[6] Bttiker M 1987 Z. Phys. B 68 161
[7] van Kampen N G 1988 IBM J. Res. Dev. 32 107
[8] Landauer R 1988 J. Stat. Phys. 53 233
[9] van den Broeck C, Kawai R 2006 Phys. Rev. Lett. 96 210601
[10] Li N, Zhan F, Hanggi P, Li B 2009 Phys. Rev. E 80 011125
[11] Li N, Hanggi P, Li B 2008 Europhys. Lett. 84 40009
[12] Asfaw M, Bekele M 2004 Eur. Phys. J. B 38 457
[13] Asfaw M, Bekele M 2005 Phys. Rev. E 72 056109
[14] Asfaw M, Bekele M 2007 Physica A 384 346
[15] Derényi I, Astumian R D 1999 Phys. Rev. E 59 R6219
[16] Zhang Y P, He J Z, He X 2010 Commun. Theor. Phys. 54 857
[17] Zhang Y P, He J Z, Ouyang H 2010 Phys. Scr. 82 055005
[18] Zhang Y P, He J Z 2010 Chin. Phys. Lett. 27 090502
[19] Luo X G, Liu N, He J Z 2013 Phys. Rev. E 87 022139
[20] Hondou T, Sekimoto K 2000 Phys. Rev. E 62 6021
[21] Ai B Q, Xie H Z, Wen D H 2005 Eur. Phys. J. B 48 101
[22] Ai B Q, Wang L Q, Liu L G 2006 Phys. Lett. A 352 286
[23] Ai B Q, Wang X J, Liu G T 2003 Phys. Rev. E 68 061105
[24] Zhang Y, Lin B H, Chen J C 2006 Eur. Phys. J. B 53 481
[25] Lin B H, Chen J C 2009 J. Phys. A: Math. Theor. 42 075006
[26] Ding Z M, Chen L G, Sun F R 2010 Braz. J. Phys. 40 141
[27] Ding Z M, Chen L G, Sun F R 2010 Sci. China G: Phys. Mech. Astron. 40 16 (in Chiese) [丁泽民, 陈林根, 孙丰瑞 2010 中国科学 G辑: 物理学 力学 天文学 40 16]
[28] Asfaw M 2008 Eur. Phys. J. B 65 109
[29] Asfaw M 2014 Phys. Rev. E 89 012143
[30] Cheng H T, He J Z, Xiao Y L 2012 Acta Phys. Sin. 61 010502 (in Chinese) [程海涛, 何济洲, 肖宇玲 2012 61 010502]
[31] Sancho J M, Miguel M S, Drr D 1982 J. Stat. Phys. 28 291
[32] Gao T F, Zhang Y, Chen J C 2009 Chin. Phys. B 18 3279
[33] Gordon J M, Huleihil M 1992 J. Appl. Phys. 72 829
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