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The interaction of work and heat between Brownian particles in a bistable system, the external periodic force and the thermal stochastic force are analyzed. The stochastic energy balance equation based on Langevin equation is established. For the Langevin equation subjected to periodic force, stochastic force and damping force, the method of combining dynamics and non-equilibrium thermodynamics is used. From force as the foothold changed into energy as the research core, the exchange of energy between system and environment and the efficiency of doing work are deeply analyzed with this method when the Brownian particle motion is along single trajectories, which reveals that the bistable system exhibits stochastic energetic resonance phenomenon.
[1] Benzi R, Sutera A, Vulpiana A 1981 Physica A 14 L453
[2] Gammaitoni L, Hanggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[3] [4] [5] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese)[胡 岗 1994 随机力与非线性系统 (上海 : 上海科技教育出版社)]
[6] Nozaki D, Mar D J, Grigg P, Collins J J 1999 Phys. Rev. Lett. 82 2402
[7] [8] Qin G R, Gong D C, Hu G, Wen X D 1992 Acta Phys. Sin. 41 360 (in Chinese)[秦光戎、 龚德纯、 胡 岗、 温孝东 1992 物理学报 41 360]
[9] [10] Lin M, Huang Y M 2006 Acta Phys. Sin. 55 3277 (in Chinese)[林 敏、 黄咏梅 2006 物理学报 55 3277]
[11] [12] Jin G X, Zhang L Y, Cao L 2009 Chin. Phys. B 18 952
[13] [14] [15] Zhu H J, Li R, Wen X D 2003 Acta Phys. Sin. 52 2404 (in Chinese)[祝恒江、 李 蓉、 温孝东 2003 物理学报 52 2404]
[16] Lin M, Mao Q M, Zheng Y J, Li D S 2007 Acta Phys. Sin. 56 5021 (in Chinese)[林 敏、 毛谦敏、 郑永军、 李东升 2007 物理学报 56 5021]
[17] [18] [19] Wang C J 2010 Chin. Phys. B 19 030503
[20] [21] Lin M, Fang L M, Zheng Y J 2009 Chin. Phys. B 18 1725
[22] [23] Dong X J 2010 Chin. Phys. B 19 010502
[24] [25] Lin M, Fang L M, Zhu R G 2008 Acta Phys.Sin. 57 2638 (in Chinese)[林 敏、 方利民、 朱若谷 2008 物理学报 57 2638]
[26] [27] Leng Y G, Wang T Y, Guo Y, Wang W J, Hu S G 2005 Acta Phys. Sin. 54 1118 (in Chinese)[冷永刚、 王太勇、 郭 焱、 汪文津、 胡世广 2005 物理学报 54 1118]
[28] [29] Lin M, Huang Y M 2007 Acta Phys.Sin. 56 6173 (in Chinese)[林 敏、 黄咏梅 2007 物理学报 56 6173]
[30] Dong X J 2009 Chin. Phys. B 18 70
[31] [32] [33] Zhang L, Liu L, Cao L 2010 Acta Phys. Sin. 59 1494 (in Chinese)[张 莉、 刘 立、 曹 力 2010 物理学报 59 1494]
[34] Lin L, Yan Y, Mei D C 2010 Acta Phys. Sin. 59 2240 (in Chinese)[林 灵、 闫 勇、 梅冬成 2010 物理学报 59 2240]
[35] [36] Guo Y F, Xu W, Wang L 2010 Chin. Phys. B 19 040503
[37] [38] Iwai T 2001 Physica A 300 350
[39] [40] Dan D, Jayannavar A M 2005 Physica A 345 404
[41] [42] Saikia S, Roy R, Jayannavar A M 2007 Phys. Lett. A 369 367
[43] [44] [45] Sekimoto K 2007 Phys. Rev. E 76 060103
[46] [47] Seifert U 2008 Eur. Phys. J. B 64 423
[48] Bustamante C, Liphardt J, Ritort F 2005 Phys. Today 58(7) 43
[49] -
[1] Benzi R, Sutera A, Vulpiana A 1981 Physica A 14 L453
[2] Gammaitoni L, Hanggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[3] [4] [5] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese)[胡 岗 1994 随机力与非线性系统 (上海 : 上海科技教育出版社)]
[6] Nozaki D, Mar D J, Grigg P, Collins J J 1999 Phys. Rev. Lett. 82 2402
[7] [8] Qin G R, Gong D C, Hu G, Wen X D 1992 Acta Phys. Sin. 41 360 (in Chinese)[秦光戎、 龚德纯、 胡 岗、 温孝东 1992 物理学报 41 360]
[9] [10] Lin M, Huang Y M 2006 Acta Phys. Sin. 55 3277 (in Chinese)[林 敏、 黄咏梅 2006 物理学报 55 3277]
[11] [12] Jin G X, Zhang L Y, Cao L 2009 Chin. Phys. B 18 952
[13] [14] [15] Zhu H J, Li R, Wen X D 2003 Acta Phys. Sin. 52 2404 (in Chinese)[祝恒江、 李 蓉、 温孝东 2003 物理学报 52 2404]
[16] Lin M, Mao Q M, Zheng Y J, Li D S 2007 Acta Phys. Sin. 56 5021 (in Chinese)[林 敏、 毛谦敏、 郑永军、 李东升 2007 物理学报 56 5021]
[17] [18] [19] Wang C J 2010 Chin. Phys. B 19 030503
[20] [21] Lin M, Fang L M, Zheng Y J 2009 Chin. Phys. B 18 1725
[22] [23] Dong X J 2010 Chin. Phys. B 19 010502
[24] [25] Lin M, Fang L M, Zhu R G 2008 Acta Phys.Sin. 57 2638 (in Chinese)[林 敏、 方利民、 朱若谷 2008 物理学报 57 2638]
[26] [27] Leng Y G, Wang T Y, Guo Y, Wang W J, Hu S G 2005 Acta Phys. Sin. 54 1118 (in Chinese)[冷永刚、 王太勇、 郭 焱、 汪文津、 胡世广 2005 物理学报 54 1118]
[28] [29] Lin M, Huang Y M 2007 Acta Phys.Sin. 56 6173 (in Chinese)[林 敏、 黄咏梅 2007 物理学报 56 6173]
[30] Dong X J 2009 Chin. Phys. B 18 70
[31] [32] [33] Zhang L, Liu L, Cao L 2010 Acta Phys. Sin. 59 1494 (in Chinese)[张 莉、 刘 立、 曹 力 2010 物理学报 59 1494]
[34] Lin L, Yan Y, Mei D C 2010 Acta Phys. Sin. 59 2240 (in Chinese)[林 灵、 闫 勇、 梅冬成 2010 物理学报 59 2240]
[35] [36] Guo Y F, Xu W, Wang L 2010 Chin. Phys. B 19 040503
[37] [38] Iwai T 2001 Physica A 300 350
[39] [40] Dan D, Jayannavar A M 2005 Physica A 345 404
[41] [42] Saikia S, Roy R, Jayannavar A M 2007 Phys. Lett. A 369 367
[43] [44] [45] Sekimoto K 2007 Phys. Rev. E 76 060103
[46] [47] Seifert U 2008 Eur. Phys. J. B 64 423
[48] Bustamante C, Liphardt J, Ritort F 2005 Phys. Today 58(7) 43
[49]
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