Related papers: Entropy Inequalities and Gaussian Comparisons
Motivated by the fluid/gravity correspondence, we consider the Penrose inequality in the framework of fluid dynamics. In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background.…
A general principle called "conservation of the ellipsoid of concentration" is introduced and a generalized entropic form of order 'alpha' is optimized under this principle. It is shown that this can produce a density which can act as a…
We show that Shannon's entropy--power inequality admits a strengthened version in the case in which the densities are log-concave. In such a case, in fact, one can extend the Blachman--Stam argument to obtain a sharp inequality for the…
Three equivalent characterizations of probability measures through independence criteria are given. These characterizations lead to a family of Brascamp--Lieb-type inequalities for relative entropy, determine equilibrium states and sharp…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so called…
Relative to the Gaussian measure on $\mathbb{R}^d$, entropy and Fisher information are famously related via Gross' logarithmic Sobolev inequality (LSI). These same functionals also separately satisfy convolution inequalities, as proved by…
The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given using matrix perspectives of operator convex functions. A matrix…
Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about entropic uncertainty in generalized…
Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of…
The entropic region is formed by the collection of the Shannon entropies of all subvectors of finitely many jointly distributed discrete random variables. For four or more variables, the structure of the entropic region is mostly unknown.…
We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the…
In recent years, a number of results have been developed which connect information measures and estimation measures under various models, including, predominently, Gaussian and Poisson models. More recent results due to Taborda and…
The Borell-Brascamp-Lieb inequality is a classical extension of the Pr\'ekopa-Leindler inequality, which in turn is a functional counterpart of the Brunn-Minkowski inequality. The stability of these inequalities has received significant…
We investigate what we term "generalized sup-convolutions". We show that functional inequalities that enjoy an interpretation as sup-convolution inequalities can be deduced from the special case of indicator functions corresponding to a…
We numerically investigate entropic Bell inequalities for a pair of entangled qutrits using information-theoretic distances. We show that for this class of inequalities Tsallis entropy is more suitable than Shannon as it reveals…
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory,…
Interpolation inequalities play an essential role in Analysis with fundamental consequences in Mathematical Physics, Nonlinear Partial Differential Equations (PDEs), Markov Processes, etc., and have a wide range of applications in various…
A natural link between the notions of majorization and strongly Sperner posets is elucidated. It is then used to obtain a variety of consequences, including new R\'enyi entropy inequalities for sums of independent, integer-valued random…