Related papers: Entropy and Diversity: The Axiomatic Approach
Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative…
This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other…
This book delves into the burgeoning field of quantum resource theories, a novel and vibrant area of research within quantum information science that seeks to unify diverse quantum phenomena under a single framework. By recognizing various…
The tension between qualitative theorizing and quantitative methods is pervasive in the social sciences, and poses a constant challenge to empirical research. But in science studies as an interdisciplinary specialty, there are additional…
The universal concept of complexity by the dynamic redundance paradigm and the ensuing concept of extended dynamic fractality (physics/9806002) are applied here to higher levels of complexity corresponding to living systems. After recalling…
The ``Gibbs Paradox'' refers to several related questions concerning entropy in thermodynamics and statistical mechanics: whether it is an extensive quantity or not, how it changes when identical particles are mixed, and the proper way to…
Prominent ethical and policy issues such as affirmative action and female enrollment in science and engineering revolve around the idea that diversity is good. However, even though diversity is an ambiguous concept, a precise definition is…
Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…
We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…
The notion of entropy penetrates much of science. A key feature of the all-important notion of Boltzmann-Gibbs-Shannon entropy is its extensivity (additivity over independent subsystems). However, there is a need for other quantities. In…
We introduce the algebraic entropy for endomorphisms of arbitrary abelian groups, appropriately modifying existing notions of entropy. The basic properties of the algebraic entropy are given, as well as various examples. The main result of…
The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work,…
Journal ranking is becoming more important in assessing the quality of academic research. Several indices have been suggested for this purpose, typically on the basis of a citation graph between the journals. We follow an axiomatic approach…
Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type theory, which brings new ideas into the very foundation of mathematics. On the one hand, Voevodsky's subtle and…
Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this…
Diversity measurement underpins the study of biological systems, but measures used vary across disciplines. Despite their common use and broad utility, no unified framework has emerged for measuring, comparing and partitioning diversity.…
The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…
This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of mathematical definitions and constructions. It is common in mathematical practice…