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

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

2004-07-26

arxiv.org/abs/nlin/0407056v1

Phys. Rev. E 71, 016118 (2005) (8 pages)

Nonlinear Sciences

Chaotic Dynamics

8 pages, 5 figures Submitted to PRE

Scientific paper

10.1103/PhysRevE.71.016118

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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