Coloured thermal noise-driven dynamical system: upper bound of time derivative of information entropy

In this paper we have studied the upper bound of the time derivative of information entropy for non-Markovian and thermodynamically closed system(s) using reduced model theory (RMT). The upper bound is calculated on the basis of the Fokker-Planck equation and the Schwartz inequality principle. Our calculation shows that the upper bound exhibits extremal nature in the variation of system parameters such as noise correlation time, dissipation strength. The present calculation also considers how the upper bound does change if we increase the number of auxiliary variables involved in the RMT.