Related papers: Entropy and its discontents: A note on definitions
In a recent Letter [1] a framework for estimating entropy was introduced and applied to one-dimensional and two-dimensional systems. In this Comment we show that the method is not well suited for estimating entropy in bidimensional systems…
Many important properties of quantum channels are quantified by means of entropic functionals. Characteristics of such a kind are closely related to different representations of a quantum channel. In the Jamio{\l}kowski-Choi representation,…
Probably not, because there are lots of manifestly unanthropic ways of producing entropy. We demonstrate that the Causal Entropic Principle (CEP), as a replacement for the anthropic principle to explain the properties of the observed…
Complexity measures are introduced, that quantify the change of the natural entropy fluctuations at different length scales in time-series emitted from systems operating far from equilibrium. They identify impending sudden cardiac death…
The aim of this note is to point out some observations concerning modified power entropy of $\Z$- and $\N$-actions. First, we provide an elementary example showing that this quantity is sensitive to transient dynamics, and therefore does…
Making decisions freely presupposes that there is some indeterminacy in the environment and in the decision making engine. The former is reflected on the behavioral changes due to communicating: few changes indicate rigid environments;…
A lower bound on the R\'enyi differential entropy of a sum of independent random vectors is demonstrated in terms of rearrangements. For the special case of Boltzmann-Shannon entropy, this lower bound is better than that given by the…
Generalized versions of the entropic (Hirschman-Beckner) and support (Elad-Bruckstein) uncertainty principle are presented for frames representations. Moreover, a sharpened version of the support inequality has been obtained by introducing…
We survey several notions of entropy related to a compact manifold of negative curvature, some relations between them, and the rigidity problems.
Recurrence rate, determinism, average line length, and entropy of line lengths are measures of complexity in recurrence quantification analysis, that help to understand the structure, predictability and complexity of dynamical systems. In…
We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems. The relevant uncertainty principle is…
We employ quantum relative entropy to establish the relation between the measurement uncertainty and its disturbance on a state in the presence (and absence) of quantum memory. For two incompatible observables, we present the…
We show that using nonextensive entropy can lead to spontaneous symmetry breaking when a parameter changes its value from that applicable for a symmetric domain, as in field theory. We give the physical reasons and also show that even for…
We show that the previously introduced concept of distance on statistical spaces leads to a straightforward definition of differential entropy on these statistical spaces. These spaces are characterized by the fact that their points can…
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…
Uncertainty quantification is a key aspect in many tasks such as model selection/regularization, or quantifying prediction uncertainties to perform active learning or OOD detection. Within credal approaches that consider modeling…
The uncertainty principle sets limit on our ability to predict the values of two incompatible observables measured on a quantum particle simultaneously. This principle can be stated in various forms. In quantum information theory, it is…
The aim of this paper is to discuss new results concerning some kinds of parametric extended entropies and divergences. As a result of our studies for mathematical properties on entropy and divergence, we give new bounds for the Tsallis…
Entropy dimension is an entropy-type quantity which takes values in $[0,1]$ and classifies different levels of intermediate growth rate of complexity for dynamical systems. In this paper, we consider the complexity of skew products of…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…