Abstract. Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical dynamical picture of the system under investigation. Indeed, DA minimizing effect error distilling correct ingredients its dynamics. is critical importance for analysis systems featuring sensitive dependence on initial conditions, as chaos wins over any finitely accur...

In this paper Kolomogorov entropy of a simulated cavity quantum electrodynamics in a multi-partite system consisting of eight quantum dots in interaction with one cavity mode has been estimated. It has been shown that the Kolmogorov Entropy monotonically increases with the increasing coupling strength, which is a sufficient condition for chaotic behavior under ultrastrong coupling regime. The a...

It was mentioned by Kolmogorov (1968, IEEE Trans. Inform. Theory 14, 662 664) that the properties of algorithmic complexity and Shannon entropy are similar. We investigate one aspect of this similarity. Namely, we are interested in linear inequalities that are valid for Shannon entropy and for Kolmogorov complexity. It turns out that (1) all linear inequalities that are valid for Kolmogorov com...

When nonlinear measures are estimated from sampled temporal signals with finite-length, a radius parameter must be carefully selected to avoid poor estimation. These generally derived the correlation integral, which quantifies probability of finding neighbors, i.e., pair points spaced by less than parameter. While each measure comes several specific empirical rules select value, we provide syst...

A central result that arose in applying information theory to the stochastic thermodynamics of nonlinear dynamical systems is the information-processing second law (IPSL): the physical entropy of the Universe can decrease if compensated by the Shannon-Kolmogorov-Sinai entropy change of appropriate information-carrying degrees of freedom. In particular, the asymptotic-rate IPSL precisely delinea...

The computation of the Kolmogorov entropy from a time series with a direct method involves the evaluation of the probabilities of the box sequences in the phase-space. This approach leads to a particular string matching problem. In this work an optimized algorithm is presented for the efficient computation of various estimates ICI of the Kolmogorov entropy, each obtained with a different length...

Due to long-term unpredictability of nonlinear system, based on the analysis of the bridge structure nonlinear characteristics and chaotic time series kolmogorov entropy extraction algorithm, calculate kolmogorov entropy of responding information time series to obtain the most predictable points of complex structure system state, so providing the theoretical support for predictable confidence i...

In the present study, the mixing of liquid phase in bubble column is analysed by an entropy theory. The Kolmogorov entropy factor depending on the operating parameter is estimated to evaluate the concentration profile of the solute dispersed in the dynamic two-phase system. The intensity of mixing is enunciated by the Kolmogorov entropy parameter and correlated with the degree of mixing in the ...

We show that extensive thermostatistics based on Rényi entropy and Kolmogorov–Nagumo averages can be expressed in terms of Tsallis nonextensive thermostatistics. We use this correspondence to generalize thermostatistics to a large class of Kolmogorov–Nagumo means and suitably adapted definitions of entropy. As an application, we reanalyze linguistic data discussed in a paper by Montemurro.  20...

To formalize the human judgment of rhythm complexity, we used five measures from information theory and algorithmic complexity to measure the complexity of 48 artificially generated rhythmic sequences. We compared these measurements to human prediction accuracy and easiness judgments obtained from a listening experiment, in which 32 participants guessed the last beat of each sequence. We also i...