Related papers: On some entropy functionals derived from R\'enyi i…
We leverage the Gibbs inequality and its natural generalization to R\'enyi entropies to derive closed-form parametric expressions of the optimal lower bounds of $\rho$th-order guessing entropy (guessing moment) of a secret taking values on…
We associate to the p-th R\'enyi entropy a definition of entropy power, which is the natural extension of Shannon's entropy power and exhibits a nice behaviour along solutions to the p-nonlinear heat equation in $R^n$. We show that the…
We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…
It is shown that R\'enyi statistics provides a plausible basis to describe the hadron distributions measured in high energy particle interactions. Generalized Boltzmann and gamma distributions obtained by maximization of R\'enyi entropy…
Several implications of well-known fluctuation theorems, on the statistical properties of the entropy production, are studied using various approaches. We begin by deriving a tight lower bound on the variance of the entropy production for a…
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…
There are three ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a…
The work performed on or extracted from a non-autonomous quantum system described by means of a two-point projective-measurement approach takes the form of a stochastic variable. We show that the cumulant generating function of work can be…
In this paper, following standard arguments, the maximum Renyi entropy problem for the weighted case is analyzed. We verify that under some constrains on weight function, the Student-r and Student-t distributions maximize the weighted Renyi…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…
The paper extends the analysis of the entropies of the Poisson distribution with parameter $\lambda$. It demonstrates that the Tsallis and Sharma-Mittal entropies exhibit monotonic behavior with respect to $\lambda$, whereas two generalized…
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…
We explore an asymptotic behavior of R\'enyi entropy along convolutions in the central limit theorem with respect to the increasing number of i.i.d. summands. In particular, the problem of monotonicity is addressed under suitable moment…
We investigate the dynamics of quantum entanglement after a global quench and uncover a qualitative difference between the behavior of the von Neumann entropy and higher R\'enyi entropies. We argue that the latter generically grow…
We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference…
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
We tighten the Entropy Power Inequality (EPI) when one of the random summands is Gaussian. Our strengthening is closely connected to the concept of strong data processing for Gaussian channels and generalizes the (vector extension of)…
The paper examines relationships between the conditional Shannon entropy and the expectation of $\ell_{\alpha}$-norm for joint probability distributions. More precisely, we investigate the tight bounds of the expectation of…
In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this…
We introduce R\'enyi entropy of a subsystem energy as a natural quantity which closely mimics the behavior of the entanglement entropy and can be defined for all the quantum many body systems. For this purpose, consider a quantum chain in…