3,933 research outputs found
Conditional entropy of ordinal patterns
In this paper we investigate a quantity called conditional entropy of ordinal
patterns, akin to the permutation entropy. The conditional entropy of ordinal
patterns describes the average diversity of the ordinal patterns succeeding a
given ordinal pattern. We observe that this quantity provides a good estimation
of the Kolmogorov-Sinai entropy in many cases. In particular, the conditional
entropy of ordinal patterns of a finite order coincides with the
Kolmogorov-Sinai entropy for periodic dynamics and for Markov shifts over a
binary alphabet. Finally, the conditional entropy of ordinal patterns is
computationally simple and thus can be well applied to real-world data
Thermodynamic formalism for field driven Lorentz gases
We analytically determine the dynamical properties of two dimensional field
driven Lorentz gases within the thermodynamic formalism. For dilute gases
subjected to an iso-kinetic thermostat, we calculate the topological pressure
as a function of a temperature-like parameter \ba up to second order in the
strength of the applied field. The Kolmogorov-Sinai entropy and the topological
entropy can be extracted from a dynamical entropy defined as a Legendre
transform of the topological pressure. Our calculations of the Kolmogorov-Sinai
entropy exactly agree with previous calculations based on a Lorentz-Boltzmann
equation approach. We give analytic results for the topological entropy and
calculate the dimension spectrum from the dynamical entropy function.Comment: 9 pages, 5 figure
Comment on `Universal relation between the Kolmogorov-Sinai entropy and the thermodynamic entropy in simple liquids'
The intriguing relations between Kolmogorov-Sinai entropy and self diffusion
coefficients and the excess (thermodynamic) entropy found by Dzugutov and
collaborators do not appear to hold for hard sphere and hard disks systems.Comment: 1 page revte
Kolmogorov-Sinai entropy and black holes
It is shown that stringy matter near the event horizon of a Schwarzschild
black hole exhibits chaotic behavior (the spreading effect) which can be
characterized by the Kolmogorov-Sinai entropy. It is found that the
Kolmogorov-Sinai entropy of a spreading string equals to the half of the
inverse gravitational radius of the black hole. But the KS entropy is the same
for all objects collapsing into the black hole. The nature of this universality
is that the KS entropy possesses the main property of temperature: it is the
same for all bodies in thermal equilibrium with the black hole. The
Kolmogorov-Sinai entropy measures the rate at which information about the
string is lost as it spreads over the horizon. It is argued that it is the
maximum rate allowed by quantum theory. A possible relation between the
Kolmogorov-Sinai and Bekenstein-Hawking entropies is discussed.Comment: 10 pages, no figures; this is an extended version of my paper
arXiv:0711.313
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