Related papers: A Useful Inequality for the Binary Entropy Functio…

Meixner's historical remark in 1969 "... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined...." is investigated from today's insight. Several…

In the paper, the authors establish three kinds of double inequalities for the trigamma function in terms of the exponential function to powers of the digamma function. These newly established inequalities extend some known results. The…

We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we…

In this article, we introduce an entropy based on the formal power series expansion of the Ihara Zeta function. We find a number of inequalities based on the values of the Ihara zeta function. These new entropies are applicable in symbolic…

We present an alternative derivation of the pair correlation function for simple classical fluids by using a variational approach. That approach involves the conditional probability p(3,..., N /1, 2) of an undefined system of N particles…

Two-sided bounds are explored for concentration functions and R\'enyi entropies in the class of discrete log-concave probability distributions. They are used to derive certain variants of the entropy power inequalities.

We introduce the concept of inflation word entropy for random substitutions with a constant and primitive substitution matrix. Previous calculations of the topological entropy of such systems implicitly used this concept and established…

Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…

The R{\'e}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{\'e}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital…

It is known that the Entropy Power Inequality (EPI) always holds if the random variables have density. Not much work has been done to identify discrete distributions for which the inequality holds with the differential entropy replaced by…

In this paper we investigate a notion of relative operator entropy, which develops the theory started by J.I. Fujii and E. Kamei [Math. Japonica 34 (1989), 341--348]. For two finite sequences $\mathbf{A}=(A_1,...,A_n)$ and…

In this paper, we extend the notion of microstate free entropy to the bi-free setting. In particular, using the bi-free analogue of random matrices, microstate bi-free entropy is defined. Properties essential to an entropy theory are…

In this study, the quantum R\'{e}nyi entropy power inequality of order $p>1$ and power $\kappa$ is introduced as a quantum analog of the classical R\'{e}nyi-$p$ entropy power inequality. To derive this inequality, we first exploit the…

Building on the recent work of Johnson (2007) and Yu (2008), we prove that entropy is a concave function with respect to the thinning operation T_a. That is, if X and Y are independent random variables on Z_+ with ultra-log-concave…

Numerous entropy-type characteristics (functionals) generalizing R\'enyi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and…

Shannon entropy is widely used to quantify the uncertainty of discrete random variables. But when normalized to the unit interval, as is often done in practice, it no longer conveys the alphabet sizes of the random variables being studied.…

It is shown how tools from the area of Model Theory, specifically from the Theory of o-minimality, can be used to prove that a class of functions is VC-subgraph (in the sense of Dudley, 1987), and therefore satisfies a uniform polynomial…

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…

We define the entropic bounds, i.e minimal uncertainty for pairs of unitary testers in distinguishing between unitary transformations not unlike the well known entropic bounds for observables. We show that in the case of specific sets of…

We obtain two-bound estimates for the local growth of pluri-subharmonic functions in terms of Siciak and relative extremal functions. As applications, we give simple new proofs of "Bernstein doubling inequality" and the main result in…