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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 are studied.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 upper bound of the time derivative of information entropy is derived on the basis of the Schwartz inequality principle and the definition of Shannons information entropy.The relationship between the properties of damping constant, the frequency of the oscillator, Gaussian colored noise and external periodic force and their effect on the upper bound of the time derivative of information entropy is also discussed.