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

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.

arXiv comment8 pages, 5 figures Submitted to PRE

References in corpus (12)

• Predictability: a way to characterize Complexity
• Dispersion of passive tracers in closed basins: beyond the diffusion coefficient
• On the (Boltzmann) Entropy of Nonequilibrium Systems
• Kolmogorov-Sinai entropy-rate vs. physical entropy
• Lyapunov exponents, entropy production and decoherence
• Predictability in Systems with Many Characteristic Times: The Case of Turbulence
• Chaos and Lyapunov exponents in classical and quantal distribution dynamics
• Exponentially rapid decoherence of quantum chaotic systems
• Coarse-Grained Probabilistic Automata Mimicking Chaotic Systems
• Liapunov Multipliers and Decay of Correlations in Dynamical Systems
• Trajectory versus probability density entropy
• Generalized dynamical entropies in weakly chaotic systems

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