Related papers: Entropy and Diversity: The Axiomatic Approach

We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…

The ideas of the constraint-based statistics are introduced. The axiom and six theorems of the constraint-based statistics are established.

Coarse geometry studies metric spaces on the large scale. The recently introduced notion of coarse entropy is a tool to study dynamics from the coarse point of view. We prove that all isometries of a given metric space have the same coarse…

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…

Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…

In an Introductory Physics for Life Science (IPLS) course that leverages authentic biological examples, student ideas about entropy as "disorder" or "chaos" come into contact with their ideas about the spontaneous formation of organized…

Dynamical systems of a new kind are described, which are motivated by the problem of constructing diffeomorphism invariant quantum theories. These are based on the extremization of a non-local and non-additive quantity that we call the…

A central task in analyzing complex dynamics is to determine the loci of information storage and the communication topology of information flows within a system. Over the last decade and a half, diagnostics for the latter have come to be…

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…

In this paper we aim to find a measure for the diversity of cash flows between agents in an economy. We argue that cash flows can be linked to probabilities of finding a currency unit in a given cash flow. We then use the information…

This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…

The participation coefficient is a widely used metric of the diversity of a node's connections with respect to a modular partition of a network. An information-theoretic formulation of this concept of connection diversity, referred to here…

Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…

In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited…

Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated…

A taxonomy is a standardized framework to classify and organize items into categories. Hierarchical taxonomies are ubiquitous, ranging from the classification of organisms to the file system on a computer. Characterizing the typical…

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…

Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical…

We argue here about the relevance and the ultimate unity of the Bayesian approach in a neutral and agnostic manner. Our main theme is that Bayesian data analysis is an effective tool for handling complex models, as proven by the increasing…

We have presented first an axiomatic derivation of Boltzmann entropy on the basis of two axioms consistent with two basic properties of thermodynamic entropy. We have then studied the relationship between Boltzmann entropy and information…