Related papers: Syntropy in complex systems: A complement to Shann…
In this paper, we estimate the Shannon entropy $S(f) = -\E[ \log (f(x))]$ of a one-sided linear process with probability density function $f(x)$. We employ the integral estimator $S_n(f)$, which utilizes the standard kernel density…
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…
We review a new form of entropy suggested by us, with origin in mixing of states of systems due to interactions and deformations of phase cells. It is demonstrated that this nonextensive form also leads to asymmetric maximal entropy…
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…
Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of…
Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…
This paper explores the concept of "entropy of knowledge" (EoN) as a framework for understanding the challenges and complexities of scientific discovery. Drawing from principles in thermodynamics and information theory, I propose that the…
Extropy was introduced as a dual complement of the Shannon entropy. In this investigation, we consider failure extropy and its dynamic version. Various basic properties of these measures are presented. It is shown that the dynamic failure…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
The paper examines relationships between the conditional Shannon entropy and the expectation of $\ell_{\alpha}$-norm for joint probability distributions. More precisely, we investigate the tight bounds of the expectation of…
A notion of entropy is introduced for causal fermion systems. This entropy is a measure of the state of disorder of a causal fermion system at a given time compared to the vacuum. The definition is given both in the finite and…
We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
We show that the R\'enyi entropies of single particle, extended wave functions for disordered systems contain information about the multifractal spectrum. It is shown for moments of the R\'enyi entropy, $S_{n}$, where $|n|<1$, it is…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
We present a unifying approach to the study of entropies in Mathematics, such as measure entropy, topological entropy, algebraic entropy, set-theoretic entropy. We take into account discrete dynamical systems, that is, pairs $(X,T)$, where…
The computational challenges posed by many-particle quantum systems are often overcome by mixed quantum-classical (MQC) models in which certain degrees of freedom are treated as classical while others are retained as quantum. One of the…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…
It is well known that to estimate the Shannon entropy for symbolic sequences accurately requires a large number of samples. When some aspects of the data are known it is plausible to attempt to use this to more efficiently compute entropy.…
Entropy is critically examined as a fundamental concept in contemporary science and informatics. Although the typical Shannon entropy provides a proper framework for describing the canonical ensemble, it fails to represent adequately the…