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Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic…

Machine Learning · Computer Science 2014-09-03 Luis G. Sanchez Giraldo , Murali Rao , Jose C. Principe

The concept of distinguishability lies at the heart of quantum information theory. We introduce \textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional…

High Energy Physics - Theory · Physics 2026-05-26 Mostafa Ghasemi

Since its introduction, the partial information decomposition (PID) has emerged as a powerful, information-theoretic technique useful for studying the structure of (potentially higher-order) interactions in complex systems. Despite its…

Information Theory · Computer Science 2023-12-11 Thomas F. Varley

We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…

Statistical Mechanics · Physics 2019-10-21 Piergiulio Tempesta , Henrik Jeldtoft Jensen

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…

Information Theory · Computer Science 2021-09-22 Gilad Gour , Marco Tomamichel

The entropy of an ergodic source is the limit of properly rescaled 1-block entropies of sources obtained applying successive non-sequential recursive pairs substitutions (see P. Grassberger 2002 ArXiv:physics/0207023 and D. Benedetto, E.…

Information Theory · Computer Science 2015-05-19 D. Benedetto , E. Caglioti , G. Cristadoro , M. Degli Esposti

Let $f : X\to X$ be a dominating meromorphic map on a compact K\"ahler manifold $X$ of dimension $k$. We extend the notion of topological entropy $h^l_{\mathrm{top}}(f)$ for the action of $f$ on (local) analytic sets of dimension $0\leq l…

Complex Variables · Mathematics 2018-07-18 Henry De Thélin , Gabriel Vigny

Information generating functions have been used for generating various entropy and divergence measures. In the present work, we introduce quantile based relative information generating function and study its properties. The proposed…

Statistics Theory · Mathematics 2024-12-04 Sankaran P. G. , Sunoj S. M. , Pavithra Hariharan

Recently, a new measure of information called extropy has been introduced by Lad, Sanfilippo and Agr\`o as the dual version of Shannon entropy. In the literature, Tsallis introduced a measure for a discrete random variable, named Tsallis…

Probability · Mathematics 2021-09-30 Narayanaswamy Balakrishnan , Francesco Buono , Maria Longobardi

We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality recently proposed by Pawlowski et. al. (arXiv:0905.2992). We consider two…

Trajectory Inference (TI) seeks to recover latent dynamical processes from snapshot data, where only independent samples from time-indexed marginals are observed. In applications such as single-cell genomics, destructive measurements make…

Machine Learning · Computer Science 2026-04-23 Chao Wang , Luca Nepote , Giulio Franzese , Pietro Michiardi

Inspired by the recent theory of Entropy-Transport problems and by the $\mathbf{D}$-distance of Sturm on normalised metric measure spaces, we define a new class of complete and separable distances between metric measure spaces of possibly…

Metric Geometry · Mathematics 2022-11-11 Nicoló De Ponti , Andrea Mondino

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…

Computer Vision and Pattern Recognition · Computer Science 2014-05-25 Dr. S. K. Katiyar , Arun P. V.

We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…

Data Analysis, Statistics and Probability · Physics 2007-10-24 Peter Sunehag

The deep connection between entropy and information is discussed in terms of both classical and quantum physics. The mechanism of information transfer between systems via entanglement is explored in the context of decoherence theory. The…

Quantum Physics · Physics 2021-01-05 Martin Paul Vaughan

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…

Mathematical Physics · Physics 2008-07-29 Flemming Topsoe

Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…

Probability · Mathematics 2018-01-23 Alois Pichler , Ruben Schlotter

We introduce hardness in relative entropy, a new notion of hardness for search problems which on the one hand is satisfied by all one-way functions and on the other hand implies both next-block pseudoentropy and inaccessible entropy, two…

Cryptography and Security · Computer Science 2024-11-15 Rohit Agrawal , Yi-Hsiu Chen , Thibaut Horel , Salil Vadhan

The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…

Statistical Mechanics · Physics 2008-11-26 Jörn Dunkel , Peter Talkner , Peter Hänggi

Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…

Quantum Physics · Physics 2020-01-03 R. V. Ramos