中国物理B ›› 2007, Vol. 16 ›› Issue (1): 42-46.doi: 10.1088/1009-1963/16/1/007

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Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation

蔡力1, 谢文贤2, 徐伟2   

  1. (1)College of Astronautics, Northwestern Polytechnical University, Xi' an 710072, China; (2)Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China
  • 收稿日期:2005-11-13 修回日期:2006-02-28 出版日期:2007-02-01 发布日期:2007-02-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10472091 and 10332030) and Natural Science Foundation of Shaanxi Province, China (Grant No 2003A03).

Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation

Xie Wen-Xian(谢文贤)a)†, Xu Wei(徐伟)a), and Cai Li(蔡力)b)   

  1. a Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China; b College of Astronautics, Northwestern Polytechnical University, Xi' an 710072, China
  • Received:2005-11-13 Revised:2006-02-28 Online:2007-02-01 Published:2007-02-01
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10472091 and 10332030) and Natural Science Foundation of Shaanxi Province, China (Grant No 2003A03).

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摘要： This paper shows the Fokker--Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker--Planck equation and the definition of Shannon's information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time \tau and coloured cross-correlation strength \la.

关键词: information entropy, entropy flux, entropy production, coloured cross-correlation, Fokker--Planck equation

Abstract: This paper shows the Fokker--Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker--Planck equation and the definition of Shannon's information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter $\gamma$ of the system, coloured cross-correlation time $\tau$ and coloured cross-correlation strength $\lambda$.

Key words: information entropy, entropy flux, entropy production, coloured cross-correlation, Fokker--Planck equation

中图分类号:  (Nonequilibrium and irreversible thermodynamics)

  • 05.70.Ln
05.10.Gg (Stochastic analysis methods) 05.20.Jj (Statistical mechanics of classical fluids) 05.40.Ca (Noise) 05.70.Ce (Thermodynamic functions and equations of state)