Effects of colored noise and external periodic force on the time derivative of information entropy for a damped harmonic oscillator

Abstract

In this paper we investigated the effects of Gaussian colored noise and external periodic force on the upper bound of the time derivative of information entropy for a damped harmonic oscillator. The one-dimensional non-Markovian process with Gaussian colored noise and external periodic force is stochastically equivalent to two-dimensional Markovian process. The dimension of Fokker–Planck equation is reduced by way of linear transformation. The upper bound of the time derivative of information entropy of this process is exactly obtained on the basis of the Schwartz inequality principle and the definition of Shannon’s information entropy. The present calculation can help us to further understand the interplay of Gaussian colored noise, damping constant, the frequency of the oscillator and external periodic force on the upper bound of the time derivative of information entropy.