非高斯噪声和正弦周期力激励的阻尼谐振子系统的信息熵

Information Entropy for a Damped Harmonic Oscillator with Non-Gaussian Noise and External Periodic Force

阻尼谐振子广泛应用于固体理论、量子场论、量子力学和量子光学等不同的研究领域.信息熵在研究随机系统的动力学特性方面扮演着非常重要的角色.本文对非高斯噪声和正弦周期力激励的阻尼谐振子系统的信息熵变化率进行研究.首先通过路径积分近似,把非高斯噪声近似转化为高斯色噪声,得到了系统的Fokker-Planck方程,然后利用线性变换的方法简化了系统的Fokker-Planck方程,并结合Shannon信息熵的定义和Schwartz不等式原理得出了阻尼谐振子系统的信息熵变化率上界的表达式,最后分析了非高斯噪声和系统各参数对熵变化率上界的影响.

Damped harmonic oscillators have attracted noticeable attention due to their wide application in solid theory, quantum field theory, quantum mechanics and quantum optics, etc. Information entropy plays an important role in the study of the properties of stochastic dynamical systems. In this paper, we discuss the effects of non-Gaussian noise and external periodic force on the upper bound of the time derivative of information entropy for a damped harmonic oscillator. We transform the non-Gaussian noise into Gaussian noise by using the path integral approximation. The dimension of the Fokker-Planck equation is reduced through the linear transformation. Based on the definition of Shannon’s information entropy and Schwartz inequality principle, we obtain the upper bound of the time derivative of information entropy of this system. Finally, we analyz the influence of non-Gaussian noise and system parameters on the upper bound of the time derivative of information entropy.