Effects of Gaussian colored noise on time evolution of information entropy in a damped harmonic oscillator

• We studied the effects of Gaussian colored noise on a damped harmonic oscillator.
• One-dimensional non-Markovian process is stochastically equivalent to two-dimensional Markovian process.
• The dimension of Fokker–Planck equation is reduced by the linear transformation.
• The exact expression of the time dependence of information entropy is derived.
• The present calculation can be used to interpret the interplay of noise on information entropy.

The effects of Gaussian colored noise on time evolution of information entropy in a damped harmonic oscillator are studied in this paper. The one-dimensional non-Markovian process with Gaussian colored noise is stochastically equivalent to two-dimensional Markovian process and the dimension of Fokker–Planck equation is reduced by the linear transformation. The exact expression of the time dependence of information entropy is derived on the basis of Fokker–Planck equation and the definition of Shannon’s information entropy. The relationship between the properties of damping constant, the frequency of the oscillator and Gaussian colored noise and their effect on time evolution of information entropy is also discussed.