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

Massimo Falcioni·Luigi Palatella·Angelo Vulpiani
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Abstract

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 pseudo-chaos. The basic reason of this fact 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.

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Massimo Falcioni, Luigi Palatella, Angelo Vulpiani. 2004-07-26. The production rate of the coarse grained Gibbs entropy and the Kolmogorov-Sinai entropy: a real connection ?. https://doi.org/10.1103/physreve.71.016118

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