Related papers: Shannon Entropy Applied to the Planar Restricted T…
In this paper, we present an application of the Shannon entropy in the case of the planar (non-restricted) four-body problem. Specifically, the Kepler-60 extrasolar system is being investigated with a primary interest in the resonant…
Based on the value of the orbital eccentricity of a particle and also its proximity to the exact resonant orbit in a three-body system, the Pendulum Approximation (Dermott & Murray 1983) or the Second Fundamental Model of Resonance (Andoyer…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…
The problem of Shannon entropy estimation in countable infinite alphabets is addressed from the study and use of convergence results of the entropy functional, which is known to be discontinuous with respect to the total variation distance…
We compute the strengths of zero-th order (in eccentricity) three-body resonances for a co-planar and low eccentricity multiple planet system. In a numerical integration we illustrate that slowly moving Laplace angles are matched by…
We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain…
In the present work we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when…
Purpose: Chaotic diffusion in the non-linear systems is commonly studied in the action framework. In this paper, we show that the study in the frequency domain provides good estimates of the sizes of the chaotic regions in the phase space,…
We calculate Shannon information entropy of trapped interacting bosons in both the position and momentum spaces, $S_r$ and $S_k$ respectively. The total entropy maintains the fuctional form $S=a + b \ln N$ for repulsive bosons. At the…
We propose a novel method for testing isotropy of a three-dimensional distribution using Shannon entropy. We test the method on some Monte Carlo simulations of isotropic and anisotropic distributions and find that the method can effectively…
Reliable data-driven estimation of Shannon entropy from small data sets, where the number of examples is potentially smaller than the number of possible outcomes, is a critical matter in several applications. In this paper, we introduce a…
We find a novel characteristic for chaotic motion by introducing Shannon entropy for periodic orbits, quasiperiodic orbits, and chaotic orbits.We compare our approach with the previous methods including Poincar\'{e} Section, Lyapunov…
The new estimates of the conditional Shannon entropy are introduced in the framework of the model describing a discrete response variable depending on a vector of d factors having a density w.r.t. the Lebesgue measure in R^d. Namely, the…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
We present a study of the equilibration process of nonequilibrium systems by means of molecular dynamics simulation technique. The nonequilibrium conditions are achieved in systems by defining velocity components of the constituent atoms…
The goal of this paper is to obtain an approximate solution of the restricted three-body problem in the case of small perturbations in the vicinity of, but not in exact resonance. In this paper, we study the restricted threebody problem…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…
We introduce a new quantity to petrology, the Shannon entropy, as a tool for quantifying mixing as well as the rate of production of hybrid compositions in the mixing system. The Shannon entropy approach is applied to time series numerical…
The fractional order generalization of Shannon entropy proposed by Ubriaco has been studied for discrete distributions. In the current paper, we conduct a detailed study of the continuous analogue of this entropy termed as fractional…