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)
a Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China; b College of Astronautics, Northwestern Polytechnical University, Xi' an 710072, China
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 $\lambda$.
Received: 13 November 2005
Revised: 28 February 2006
Accepted manuscript online:
Fund: 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).
Cite this article:
Xie Wen-Xian(谢文贤), Xu Wei(徐伟), and Cai Li(蔡力) Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation 2007 Chinese Physics 16 42
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