The production rate of the coarse grained Gibbs entropy and the Kolmogorov-Sinai entropy: a real connection?

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We discuss the connection between the Kolmogorov-Sinai entropy, hKS, and the production rate of the coarse grained Gibbs entropy, rG. Detailed numerical computations show that the (often accepted) identification of the two quantities does not hold in systems with intermittent behavior and/or very different characteristic times and in systems presenting pseudo-chaos. The basic reason of this fact is in the asymptotic (with respect to time) nature of hKS, while rG is a quantity related to short time features of a system.