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This paper introduces "swiveled Renyi entropies" as an alternative to the Renyi entropic quantities put forward in [Berta et al., Phys. Rev. A 91, 022333 (2015)]. What distinguishes the swiveled Renyi entropies from the prior proposal of…

Quantum Physics · Physics 2016-03-22 Frédéric Dupuis , Mark M. Wilde

We discuss basic statistical properties of systems with multifractal structure. This is possible by extending the notion of the usual Gibbs--Shannon entropy into more general framework - Renyi's information entropy. We address the…

Statistical Mechanics · Physics 2007-05-23 Petr Jizba , Toshihico Arimitsu

In this paper we prove a convexity property of the relative entropy along entropic interpolations (solutions of the Schr\"odinger problem), and a regularity property of the entropic cost along the heat flow. Then we derive a dimensional EVI…

Analysis of PDEs · Mathematics 2017-11-23 Luigia Ripani

Explicit rate of convergence in variance (or more general entropies) is obtained for a class of Piecewise Deterministic Markov Processes such as the TCP process, relying on functional inequalities. A method to establish Poincar\'e (and more…

Probability · Mathematics 2015-09-14 Pierre Monmarché

In this paper we give some sharper refinements and generalizations of inequalities related to Shafer's inequality for the arctangent function, stated in Theorems 1, 2 and 4 in [1], by C. Mortici and H.M. Srivastava.

Classical Analysis and ODEs · Mathematics 2019-10-15 Branko Malesevic , Marija Rasajski , Tatjana Lutovac

We consider the generalization of the Araki-Uhlmann formula for relative entropy to Petz-R\'enyi relative entropy. We compute this entropy for a free scalar field in the Minkowski wedge between the vacuum and a coherent state, as well as…

Mathematical Physics · Physics 2025-03-18 Markus B. Fröb , Leonardo Sangaletti

We investigate the large-time asymptotics of nonlinear diffusion equations $u_t = \Delta u^p$ in dimension $n \ge 1$, in the exponent interval $p > n/(n+2)$, when the initial datum $u_0$ is of bounded second moment. Precise rates of…

Analysis of PDEs · Mathematics 2015-06-19 J. A. Carrillo , G. Toscani

Thanks to Pfaffian techniques, we study the R\'enyi entanglement entropies and the entanglement spectrum of large subsystems for two-dimensional Rokhsar-Kivelson wave functions constructed from a dimer model on the triangular lattice. By…

Statistical Mechanics · Physics 2012-02-13 Jean-Marie Stéphan , Grégoire Misguich , Vincent Pasquier

Systems with a long-term stationary state that possess as a spatio-temporally fluctuation quantity $\beta$ can be described by a superposition of several statistics, a "super statistics". We consider first, the Gamma, log-normal and…

Statistical Mechanics · Physics 2015-06-05 O. Obregón , A. Gil-Villegas

General extensions of an inequality due to Rogozin, concerning the essential supremum of a convolution of probability density functions on the real line, are obtained. While a weak version of the inequality is proved in the very general…

Probability · Mathematics 2017-05-03 Mokshay Madiman , James Melbourne , Peng Xu

We show a general phenomenon of the constrained functional value for densities satisfying general convexity conditions, which generalizes the observation in Bobkov and Madiman (2011) that the entropy per coordinate in a log-concave random…

Information Theory · Computer Science 2020-10-27 Yanjun Han

We consider the generalized differential entropy of normalized sums of independent and identically distributed (IID) continuous random variables. We prove that the R\'{e}nyi entropy and Tsallis entropy of order $\alpha\ (\alpha>0)$ of the…

Information Theory · Computer Science 2011-06-20 Hongfei Cui , Jianqiang Sun , Yiming Ding

There are no universally accepted definitions of R\'enyi conditional entropy and R\'enyi mutual information, although motivated by different applications, several definitions have been proposed in the literature. In this paper, we consider…

Information Theory · Computer Science 2025-11-05 Shi-Bing Li , Ke Li , Lei Yu

We establish a general connection between entropic uncertainty relations, Einstein-Podolsky-Rosen steering, and joint measurability. Specifically, we construct steering inequalities from any entropic uncertainty relation, given that the…

Quantum Physics · Physics 2018-12-20 Tamás Kriváchy , Florian Fröwis , Nicolas Brunner

The paper is concerned with proving the equivalence of convexity or concavity properties of thermodynamic functions, such as energy and entropy, depending on different sets of variables. These variables are the basic thermodynamic state…

Analysis of PDEs · Mathematics 2025-10-29 Mária Lukáčová-Medvid'ová , Ferdinand Thein , Gerald Warnecke , Yuhuan Yuan

In this paper, we provide the R\'enyi entropy and complexity measure for a novel, flexible class of skew-gaussian distributions and their related families, as a characteristic form of the skew-gaussian Shannon entropy. We give closed…

Data Analysis, Statistics and Probability · Physics 2016-05-10 Javier E. Contreras-Reyes

This work explores properties of Strong Data-Processing constants for R\'enyi Divergences. Parallels are made with the well-studied $\varphi$-Divergences, and it is shown that the order $\alpha$ of R\'enyi Divergences dictates whether…

Information Theory · Computer Science 2026-01-15 Adrien Vandenbroucque , Amedeo Roberto Esposito , Michael Gastpar

Our aim is to provide a short and self contained synthesis which generalise and unify various related and unrelated works involving what we call Phi-Sobolev functional inequalities. Such inequalities related to Phi-entropies can be seen in…

Probability · Mathematics 2021-11-30 Djalil Chafai

This article is a continuation of my paper [arxiv: 1409.1015v2]. R\'enyi and Tsallis entropies are associated to positive linear operators and properties of some functions related to these entropies are investigated.

Classical Analysis and ODEs · Mathematics 2014-12-17 Ioan Raşa

A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the…

Strongly Correlated Electrons · Physics 2024-02-20 Siqi Shao , Yashar Komijani