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周期性双势垒锯齿势中温差驱动的布朗热机

程海涛 何济洲 肖宇玲

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周期性双势垒锯齿势中温差驱动的布朗热机

程海涛, 何济洲, 肖宇玲

Brownian heat engine driven by temperature difference in a periodic double-barrier sawtooth potential

Cheng Hai-Tao, He Ji-Zhou, Xiao Yu-Ling
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  • 研究了周期性双势垒锯齿势中, 布朗粒子在外力作用下沿空间坐标方向交替地和高、低温热库接触构成的布朗热机的热力学性能. 考虑布朗粒子动能的变化以及高、 低温库之间热漏的存在, 通过数值计算分析势垒高度、势比、外力等参数对布朗热机效率的影响. 研究表明:当考虑热漏时, 布朗热机始终是不可逆的, 效率小于卡诺效率; 并且当热漏很小时, 势比的增大在一定程度上可提高布朗热机的效率; 其功率与效率之间的关系曲线为闭合线. 当不考虑热漏时, 其功率与效率之间的关系曲线为开型线, 但由于布朗粒子动能的变化引起的不可逆热流, 热机的效率依然小于卡诺效率.
    This paper has studied the thermodynamic performance of a Brownian heat engine, which is driven by temperature difference. Brownian particles move in the periodic double-barrier sawtooth potential with an external load force and contact with 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 influence of the main parameters, including the height of barrier, the ratio of the low barrier to high barrier and the external load force, on the efficiency of Brownian heat engine is discussed in detail. When the heat leak between the two reservoirs is taken into account, the Brownian heat engine is irreversible, the efficiency is less than the Carnot efficiency. When the heat leak is small, the ratio of the low barrier to high barrier can increase the efficiency. The curve of the power output versus the efficiency is a loop-shaped one. When the heat leak is negligible, the curve of the power output versus the efficiency is an open-shaped one. The efficiency is still less than the Carnot efficiency, because the heat flow via kinetic energy change of the particles is irreversible.
    • 基金项目: 国家自然科学基金(批准号:11065008)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11065008).
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    Asfaw M, Bekele M 2004 Eur. Phys. J. B 38 457

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    Asfaw M, Bekele M 2005 Phys. Rev. E 72 056109

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    Asfaw M, Bekele M 2007 Physica A 384 346

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    Hondou T, Sekimoto K 2000 Phys. Rev. E 62 6021

    [17]

    Ai B Q, Xie H Z, Wen D H, Liu X M, Liu L G 2005 Eur. Phys. J. B 48 101

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    Ai B Q, Wang L Q, Liu L G 2006 Phys. Lett. A 352 286

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    Zhang Y, Lin B H, Chen J C 2006 Eur. Phys. J. B 53 481

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    Lin B H, Chen J C 2009 J. Phys. A: Math. Theor. 42 075006

    [21]

    Zhang Y P, He J Z, He X, Xiao Y L 2010 Commun. Theor. Phys. 54 857

    [22]

    Zhang Y P, He J Z 2010 Chin. Phys. Lett. 27 090502

    [23]

    Zhang Y P, He J Z, Ouyang H, Qian X X 2010 Phys. Scr. 82 055005

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    Ding Z M, Chen L G, Sun F R 2010 Braz. J. Phys. 40 141

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    [26]

    Gao T F, Zhang Y, Chen J C 2009 Chin. Phys. B 18 3279

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    Asfaw M 2008 Eur. Phys. J. B 65 109

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  • [1]

    Reimann P 2002 Phys. Rep. 361 57

    [2]

    Astumian R D, Hänggi P 2002 Phys. Today 55 33

    [3]

    Van den Broeck C, Kawai R, Meurs P 2004 Phys. Rev. Lett. 93 090601

    [4]

    Parrondo J M R, Blanco J M, Cao F J, Brito R 1998 Europhys. Lett. 43 248

    [5]

    Parrondo J M R, de Cisneros B J 2002 Appl. Phys. A 75 179

    [6]

    Bouzat S, Wio H S 2004 Eur. Phys. J. B 41 97

    [7]

    Feynman R P, Leighton R B, SandsM1966 The Feynman Lectures on Physics I (Reading MA: Addison-Wesley) 46.1–46.9

    [8]

    Velasco S, Roco J M M, Medina A, Calvo Hernández A 2001 J. Phys. D: Appl. Phys. 34 1000

    [9]

    Büttiker M 1987 J. Phys. B 68 161

    [10]

    van Kampen N G 1988 IBM J. Res. Dev. 32 107

    [11]

    Landauer R 1988 J. Stat. Phys. 53 233

    [12]

    Derényi I, Astumian R D 1999 Phys. Rev. E 59 R6219

    [13]

    Asfaw M, Bekele M 2004 Eur. Phys. J. B 38 457

    [14]

    Asfaw M, Bekele M 2005 Phys. Rev. E 72 056109

    [15]

    Asfaw M, Bekele M 2007 Physica A 384 346

    [16]

    Hondou T, Sekimoto K 2000 Phys. Rev. E 62 6021

    [17]

    Ai B Q, Xie H Z, Wen D H, Liu X M, Liu L G 2005 Eur. Phys. J. B 48 101

    [18]

    Ai B Q, Wang L Q, Liu L G 2006 Phys. Lett. A 352 286

    [19]

    Zhang Y, Lin B H, Chen J C 2006 Eur. Phys. J. B 53 481

    [20]

    Lin B H, Chen J C 2009 J. Phys. A: Math. Theor. 42 075006

    [21]

    Zhang Y P, He J Z, He X, Xiao Y L 2010 Commun. Theor. Phys. 54 857

    [22]

    Zhang Y P, He J Z 2010 Chin. Phys. Lett. 27 090502

    [23]

    Zhang Y P, He J Z, Ouyang H, Qian X X 2010 Phys. Scr. 82 055005

    [24]

    Ding Z M, Chen L G, Sun F R 2010 Braz. J. Phys. 40 141

    [25]

    Ding Z M, Chen L G, Sun F R 2010 Sci. China: Phys. Mech. Astron. 40 16 (in Chinese) [?L?, ? ?, ?á 2010 ¥I ??:?n? ?? U?? 40 16]

    [26]

    Gao T F, Zhang Y, Chen J C 2009 Chin. Phys. B 18 3279

    [27]

    Asfaw M 2008 Eur. Phys. J. B 65 109

    [28]

    Sancho J M, Miguel M S, Durr D 1982 J. Stat. Phys. 28 291

    [29]

    Yan Z J, Chen J C 1990 J. Phys. D: Appl. Phys. 23 136

    [30]

    Chen J C 1997 J. Phys. D: Appl. Phys. 30 582

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出版历程
  • 收稿日期:  2011-04-02
  • 修回日期:  2011-05-04
  • 刊出日期:  2012-01-05

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