On entropy rates of dynamical systems and Gaussian processes

The possibility of a relation between the Kolmogorov-Sinai entropy of a dynamical system and the entropy rate of a Gaussian process isospectral to time series generated by the dynamical system is numerically investigated using discrete and continuous chaotic dynamical systems. The results suggest that such a relation as a nonlinear one-to-one function may exist when the Kolmogorov-Sinai entropy varies smoothly with variations of the system parameters, but is broken in critical states near bifurcation points.