关键词: 非高斯噪声, 阻尼谐振子, 信息熵, Fokker-Planck方程

Abstract: 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.

Key words: non-Gaussian noise, damping harmonic oscillator, information entropy, Fokker-Planck equation