Related papers: A new entropy power inequality for integer-valued …
In statistical physics, if we successively divide an equilibrium system into two parts, we will face a situation that, within a certain length $\xi$, the physics of a subsystem is no longer the same as the original system. Then the…
The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…
We give a counterexample to the vector generalization of Costa's entropy power inequality (EPI) due to Liu, Liu, Poor and Shamai. In particular, the claimed inequality can fail if the matix-valued parameter in the convex combination does…
We calculate the R\'enyi entropy of a positive integer order $M$ for a reduced density matrix of a single-level quantum dot connected to left and right leads. We exploit a $2 \times 2$ modified Keldysh Green function matrix obtained by the…
A recent result presented the expansion for the entropy rate of a Hidden Markov Process (HMP) as a power series in the noise variable $\eps$. The coefficients of the expansion around the noiseless ($\eps = 0$) limit were calculated up to…
We improve the classical discrete Hardy inequality for $ 1<p<\infty $ for functions on the natural numbers. For integer values of $ p $ the Hardy weight is an absolutely monotonic function.
We extend the Jarzynski equality, which is an exact identity between the equilibrium and nonequilibrium averages, to be useful to compute the value of the entropy difference by changing the Hamiltonian. To derive our result, we introduce…
We show that the Entropy Photon-Number Inequality (EPnI) holds where one of the input states is the vacuum state and for several candidates of the other input state that includes the cases when the state has the eigenvectors as the number…
We introduce a canonical notion of entropy for polynomials analogue to that of random variables in probability. We prove that entropy increases smoothly with respect to finite free addition. In particular we get the new inequality : $…
The aim of this paper is to discuss new results concerning some kinds of parametric extended entropies and divergences. As a result of our studies for mathematical properties on entropy and divergence, we give new bounds for the Tsallis…
It was recently shown that estimating the Shannon entropy $H({\rm p})$ of a discrete $k$-symbol distribution ${\rm p}$ requires $\Theta(k/\log k)$ samples, a number that grows near-linearly in the support size. In many applications $H({\rm…
Neural networks and other machine learning models compute continuous representations, while humans communicate with discrete symbols. Reconciling these two forms of communication is desirable to generate human-readable interpretations or to…
This paper describes an entropy equation, but one that should be used for measuring energy and not information. In relation to the human brain therefore, both of these quantities can be used to represent the stored information. The human…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
The recent introduction of geometric partition entropy brought a new viewpoint to non-parametric entropy quantification that incorporated the impacts of informative outliers, but its original formulation was limited to the context of a…
Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index on the other hand is an established…
Let $E_0,\ldots,E_n$ be a partition of the set of prime numbers, and define $E_j(x) := \sum_{p \in E_j \atop p \leq x} \frac{1}{p}$. Define $\pi(x;\mathbf{E},\mathbf{k})$ to be the number of integers $n \leq x$ with $k_j$ prime factors in…
The entropic doubling $\sigma_{\operatorname{ent}}[X]$ of a random variable $X$ taking values in an abelian group $G$ is a variant of the notion of the doubling constant $\sigma[A]$ of a finite subset $A$ of $G$, but it enjoys somewhat…
This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…
Both complete decoupling and tangent decoupling are classical tools aiming to compare two random processes where one has a weaker dependence structure. We give a new proof for the complete decoupling inequality, which provides a lower bound…