Related papers: Three tutorial lectures on entropy and counting
We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…
We introduce the algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as the natural extension of the algebraic entropy for endomorphisms of discrete vector spaces. We show that the…
This is the monograph on the theory and applications of copula entropy (CE). This book first introduces the theory of CE, including its background, definition, theorems, properties, and estimation methods. The theoretical applications of CE…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
This work demonstrates how the concept of the entropic potential of events -- a parameter quantifying the influence of discrete events on the expected future entropy of a system -- can enhance uncertainty quantification, decision-making,…
Polydisperse systems are commonly encountered when dealing with soft matter in general or any non simple fluid. Yet their treatment within the framework of statistical thermodynamics is a delicate task as the latter has been essentially…
The channel output entropy of a transmitted word is the entropy of the possible channel outputs and similarly, the input entropy of a received word is the entropy of all possible transmitted words. The goal of this work is to study these…
The goal of this paper is to develop an estimate for the entropy of random long-range correlated symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov…
Information-theoretic measures such as relative entropy and correlation are extremely useful when modeling or analyzing the interaction of probabilistic systems. We survey the quantum generalization of 5 such measures and point out some of…
Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation.…
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…
These lectures on the combinatorics and geometry of 0/1-polytopes are meant as an \emph{introduction} and \emph{invitation}. Rather than heading for an extensive survey on 0/1-polytopes I present some interesting aspects of these objects;…
This paper proposes that the mathematical relationship between an entropy distribution and its limit offers some new insight into system performance. This relationship is used to quantify variation among the entities of a system, where…
These are notes from a three-lecture mini-course on free probability given at MSRI in the Fall of 2010 and repeated a year later at Harvard. The lectures were aimed at mathematicians and mathematical physicists working in combinatorics,…
The aim of this note is to introduce a notion of dynamical entropy, which we call infinite-product entropy, for probability measures on (countable) infinite cartesian product of any measurable space with itself. The idea behind the…
An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to…
In this short note we study the entropy for algebraic actions of certain amenable groups. The possible values for this entropy are studied. Various fundamental results about certain classes of amenable groups are reproved using elementary…
This paper presents the notion of a variation entropy. This concept is an entropy framework for the gradient of the solution of a conservation law instead of on the solution itself. It appears that all semi-norms are admissible variation…