Upper bound for the time derivative of entropy for a dynamical system driven by coloured cross-correlated white noises
Xie Wen-Xian (谢文贤)a, Xu Wei (徐伟)a, Cai Li (蔡力)b, Jin Yan-Fei (靳艳飞)a
a Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072, China; b College of Astronautics, Northwestern Polytechnical University, Xi' an 710072, China
Abstract It is shown how the cross-correlation time and strength of coloured cross-correlated white noises can set an upper bound for the time derivative of entropy in a nonequilibrium system. The value of upper bound can be calculated directly based on the Schwartz inequality principle and the Fokker--Planck equation of the dynamical system driven by coloured cross-correlated white noises. The present calculations can be used to interpret the interplay of the dissipative constant and cross-correlation time and strength of coloured cross-correlated white noises on the upper bound.
Received: 15 March 2005
Revised: 18 April 2005
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 10472091 and 10332030), the Natural Science Foundation of Shaanxi Province of China (Grant No 2003A03).
Cite this article:
Xie Wen-Xian (谢文贤), Xu Wei (徐伟), Cai Li (蔡力), Jin Yan-Fei (靳艳飞) Upper bound for the time derivative of entropy for a dynamical system driven by coloured cross-correlated white noises 2005 Chinese Physics 14 1766
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