Kolmogorov entropy

Further work is needed to determine in which regimes, if any, fluid bed behave as chaotic systems. Additional testing is needed to determine the sensitivity of important bed hydrodynamic characteristics to the Kolmogorov entropy, to quantitatively relate changes of entropy to... 

RMT). K systems are most strongly mixing classical systems with a positive Kolmogorov entropy. The conjecture turned out valid also for less chaotic (ergodic) systems without time-reversal invariance leading to the Gaussian unitary ensemble (GUE). 

Kolmogorov entropy — Entropy is related to the amount of information needed to locate a system in... 

Fig. 17. The transition to chaos (from a to d) observed in the work function during CO oxidation on Pt(l 10) while decreasing CO pressure. Chaos in the upper time series (d) was characterized by the Liapunov exponent, Kolmogorov entropy, and the embedding dimension (From Ref. 68.)...

We briefly mention a couple of interesting papers that are directly related to chaos and transport. Ihm et u/.184 demonstrate that the Kolmogorov entropy r KS is related to the self-diffusion coefficient (D) in simple liquids by the relationship... 

III. Power Spectra, Phase-Space Dimensions, Liapunov Exponents, and Kolmogorov Entropy... 

We may look at atomic clusters as particularly apt and useful models to study virtually every aspect of what we call, diffusely, complexity. Simulations are particularly powerful means to carry out such studies. For example, we can follow trajectories for very long times with molecular dynamics and thereby evaluate the global means of the exponential rates of divergence of neighboring trajectories. This is the most common way to evaluate those exponents, the Liapunov exponents. The sum of these is the Kolmogorov entropy, one gross measure of the volume of phase space that the system explores, and hence one... 

III. POWER SPECTRA, PHASE-SPACE DIMENSIONS, LIAPUNOV EXPONENTS, AND KOLMOGOROV ENTROPY... 

Next, we turn to the Liapunov exponents and the Kolmogorov entropy (K-entropy). The systems concerning us here are Hamiltonian, so the Liapunov... 

The fact that the deviation is smaller for saddle I than that for saddle II implies that the crossing dynamics over saddle I should exhibit better approximate invariants of motion with q than that over saddle II at (P(s ). Note that less chaotic saddle-crossing dynamics need not imply a better approximate invariant of motion associated with at any specific order of the perturbative calculation. Furthermore, the strength of chaos in the regions of saddles, as characterized by the local Kolmogorov entropy, the... 

Dh involves coverings by sets of small but perhaps widely varying size. The boxcounting dimension is sometimes also referred to as the Minkowski dimension [5], Minkowski-Bouligand dimension [4, 29, 30], Bouligand-Minkowski dimension [31], capacity dimension [5, 32] or the Kolmogorov entropy [5]. 

Nedeltchev S, Kumar SB, Dudukovic MP. (2003) Plow regime identification in a bubble column based on both Kolmogorov entropy and quality of mixedness derived from CARPT data. Can. J. Chem. Eng., 81 367-374. 

Evaluated by Kolmogorov entropy, correlation dimension, Lyapunov exponent, presence of the chaotic attractor, Hurst coefficient, etc. 

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