Entropies in case of continuous time

Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for time-continuous entropies a new possibility for the distinction of chaos and noise. In the deterministic case an upper threshold of the joint uncertainty in the limit of infinitely high sampling rate can be found and the entropy rate can be calculated as a usual time derivative of the entropy. In a three-dimensional representation the dependence of the joint entropy on space resolution, discretization time step length and uncertainty-assessed time is shown in a unified manner. Hence the dimension and the Kolmogorov-Sinai entropy rate of any dynamics can be read out as limit cases from one single graph.