色噪声驱动的双奇异随机系统随时间演化的熵变化率上界

Upper bound of the rate of entropy change of a stochastic system with double singularities driven by colored noise

通过变换的方法讨论了一类高斯色噪声驱动的双奇异随机系统所对应的Fokker-Planck方程,并结合Shannon信息熵的定义及Schwartz不等式原理给出了经变换后该系统随时间演化的熵变化率上界的精确表达式.分析了奇异性强度参数、噪声相关时间与耗散参数对熵变化率上界的显著影响.

Based on the method of transformation, this paper studies the Fokker-Planck equation of a stochastic system with double singularities driven by Gaussian colored noise. According to the definition of Shannon＇ s information entropy and the Schwartz inequality principle, the explicit time dependence of the upper bound of the rate of entropy change is obtained for the first time. The relationship between the properties of double singularities, noise correlation time and dissipative parameter and their effect on the upper bound of the rate of entropy change are discussed.