Related papers: Kolmogorov--Nagumo Mean Frameworks for Conditional…
We numerically calculate, at the edge of chaos, the time evolution of the nonextensive entropic form $S_q \equiv [1-\sum_{i=1}^W p_i^q]/[q-1]$ (with $S_1=-\sum_{i=1}^Wp_i \ln p_i$) for two families of one-dimensional dissipative maps,…
The notion of entropy is ubiquitous both in natural and social sciences. In the last two decades, a considerable effort has been devoted to the study of new entropic forms, which generalize the standard Boltzmann-Gibbs (BG) entropy and are…
While Kolmogorov's probability axioms are widely recognized, it is less well known that in an often-overlooked 1930 note, Kolmogorov proposed an axiomatic framework for a unifying concept of the mean -- referred to as regular means. This…
We present an upper bound for the Kolmogorov-Sinai entropy of quantum systems having a mixing quantum phase space. The method for this estimation is based on the following ingredients: i) the graininess of quantum phase space in virtue of…
In the case of scalar conservation laws $$ u_{t} + f(u)_{x}~=~0,\qquad t\geq 0, x\in\mathbb{R}, $$ with uniformly strictly convex flux $f$, quantitative compactness estimates - in terms of Kolmogorov entropy in ${\bf L}^{1}_{loc}$ - were…
In this paper, we establish the entropy-entropy production estimate for the ES-BGK model, a generalized version of the BGK model of the Boltzmann equation introduced for better approximation in the Navier-Stokes limit. Our result improves…
According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are…
This paper presents a unified interpretation of $\alpha$-mutual information ($\alpha$-MI) in terms of generalized $g$-leakage. Specifically, we present a novel interpretation of $\alpha$-MI within an extended framework for quantitative…
The aim of this paper is to investigate the q -> 1/q duality in an information-entropy theory of all q-generalized entropy functionals (Tsallis, Renyi and Sharma-Mittal measures) in the light of a representation based on generalized…
We address the problem of applying the Kolmogorov-Sinai method of entropic analysis, expressed in a generalized non-extensive form, to the dynamics of the logistic map at the chaotic threshold, which is known to be characterized by a power…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…
A unified combinatorial definition of the information content and entropy of different types of patterns, compatible with the traditional concepts of information and entropy, going beyond the limitations of Shannon information interpretable…
We adapt the Kolmogorov-Sinai entropy to the non-extensive perspective recently advocated by Tsallis. The resulting expression is an average on the invariant distribution, which should be used to detect the genuine entropic index Q. We…
Taking only the characteristics as absolute, in the spirit of Arnold's "Geometrical Methods in the Theory of Ordinary Differential Equations" (Springer, 1988), we give an independent of coordinates formulation of general variational entropy…
We consider deterministic particle dynamics with time evolving weights and their associated Kolmogorov equation and mean-field equation. We prove existence and unique- ness for the limit PDE alongside estimates on the growth of the…
We propose an entropy-stable conservative flux form neural network (CFN) that integrates classical numerical conservation laws into a data-driven framework using the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT)…
We use the kinetic theory of gases to compute the Kolmogorov-Sinai entropy per particle for a dilute gas in equilibrium. For an equilibrium system, the KS entropy, h_KS is the sum of all of the positive Lyapunov exponents characterizing the…
As additivity is a characteristic property of the classical information measure, Shannon entropy, pseudo-additivity is a characteristic property of Tsallis entropy. Renyi generalized Shannon entropy by means of Kolmogorov-Nagumo averages,…
Observing how long a dynamical system takes to return to some state is one of the most simple ways to model and quantify its dynamics from data series. This work proposes two formulas to estimate the KS entropy and a lower bound of it, a…