Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting rank vectors called ordinal patterns or just permutations. The reasons for increasing popularity this in analysis include that (i) it converges to Kolmogorov-Sinai underlying dynamics limit ever longer permutations, and (ii) its computation dispenses with generating ad hoc partit...

We show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable. We adopt the definition of density entropy as a functional of a distribution density whose time evolution is determined by a transport equation, conceived as the only prescription to use for the calculation. Although the ...

The flow fields in polymer processing exhibit complex behavior with chaotic characteristics, due in part to the non-linearity of the field equations describing them. In chaotic flows fluid elements are highly sensitive to their initial positions and velocities. A fundamental understanding of such characteristics is essential for optimization and design of equipment used for distributive mixing....

We propose maximizing the change of thermodynamic entropy in order to obtain the probability distributions for nonequilibrium systems in steady or stationary evolution. Arguments are forwarded to support this approach. A path information leading to Kolmogorov-Sinai entropy is defined for an ensemble of possible trajectories between two points in phase space. It is shown that the maximization of...

We study a notion of entropy for probability measure preserving actions of finitely generated free groups, called f-invariant entropy, introduced by Lewis Bowen. In the degenerate case, the f-invariant entropy is negative infinity. In this paper we investigate the qualitative consequences of having finite f-invariant entropy. We find three main properties of such actions. First, the stabilizers...

ergodic theory : Bernoulli shifts. There is a class of transformations that play a central role in ergodic theory, namely the Bernoulli shifts. The reason for this is partly because they are in a certain sense the simplest examples of measure-preserving transformations and partly because of their role in applications. Definition of Bernoulli shifts. If we are given positive numbers Pu ' ' ' » P...

Turbulent flows are known to enhance turbulent transport. It has then even been suggested that turbulence is a state of maximum energy dissipation. In this paper, we re-examine critically this suggestion in light of several recent works around the Maximum Entropy Production principle (MEP) that has been used in several out-of-equilibrium systems. We provide a set of four different optimization ...

We investigate the quantum entanglement in rapidity space of soft gluon wave function a quarkonium, theories with non-trivial evolutions. found that evolution drastically changes behavior entropy, at any given order perturbation theory. At large $N_c$, reduced density matrices "resum" leading rapidity-logs can be explicitly constructed, and shown to satisfy Balitsky-Kovchegov (BK)-like equation...