Production rate of the coarse-grained Gibbs entropy and the Kolmogorov-Sinai entropy: A real connection?

We discuss the connection between the Kolmogorov-Sinai entropy h KS and the production rate of the coarse-grained Gibbs entropy r G. 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 pseudochaos. The basic reason for this is in the asymptotic (with respect to time) nature of h KS, while r G is a quantity related to short-time features of a system. © 2005 The American Physical Society