Related papers: Statistical Inference for R\'enyi Entropy Function…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
Using R\'enyi entropy, a possible thermostatistics for nonextensive systems is discussed. We show that it is possible to get the $q$-exponential distribution function for nonextensive systems having nonadditive energy but additive entropy.…
Conventional information-theoretic quantities assume access to probability distributions. Estimating such distributions is not trivial. Here, we consider function-based formulations of cross entropy that sidesteps this a priori estimation…
We review connections between the cumulant generating function of full counting statistics of particle number and the R\'enyi entanglement entropy. We calculate these quantities based on the fermionic and bosonic path-integral defined on…
We obtain formulas for Petz-R\'enyi and Umegaki relative entropy from the idea of distribution of a positive selfadjoint operator. Classical results on R\'enyi and Kullback-Leibler divergences are applied to obtain new results and new…
A method is presented for computing the R\'enyi entropy of a perturbed massless vacuum on the ball via a comparison with lattice field theory. If the perturbed state is Gaussian with smoothly varying correlation functions and the…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
We introduce and study generalized R\'enyi entropies defined through the traces of products of ${\rm Tr}_B (|\Psi_i\rangle\langle \Psi_j|)$ where $|\Psi_i\rangle$ are eigenstates of a two-dimensional conformal field theory (CFT). When…
R\'enyi complexity ratio of two density functions is introduced for three and multidimensional quantum systems. Localization property of several density functions are defined and five theorems about near continuous property of R\'enyi…
In many applications, the probability density function is subject to experimental errors. In this work the continuos dependence of a class of generalized entropies on the experimental errors is studied. This class includes the C. Shannon,…
We present a general method for calculating R\'enyi entropies in the ground state of a one-dimensional critical system with mixed open boundaries, for an interval starting at one of its ends. In the conformal field theory framework, this…
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…
A general investigation is made into the intrinsic Riemannian geometry for complex systems, from the perspective of statistical mechanics. The entropic formulation of statistical mechanics is the ingredient which enables a connection…
Shannon entropy for discrete distributions is a fundamental and widely used concept, but its continuous analogue, known as differential entropy, lacks essential properties such as positivity and compatibility with the discrete case. In this…
We study the problem of detecting the structure of a complex dynamical system described by a set of deterministic differential equation that contains a Hamiltonian subsystem, without any information on the explicit form of evolution laws.…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
Configurational entropy, or complexity, plays a critical role in characterizing disordered systems such as glasses, yet its measurement often requires significant computational resources. Recently, R\'enyi entropy, a one-parameter…
Data partitioning that maximizes/minimizes the Shannon entropy, or more generally the R\'enyi entropy is a crucial subroutine in data compression, columnar storage, and cardinality estimation algorithms. These partition algorithms can be…
A class of estimators of the R\'{e}nyi and Tsallis entropies of an unknown distribution $f$ in $\mathbb{R}^m$ is presented. These estimators are based on the $k$th nearest-neighbor distances computed from a sample of $N$ i.i.d. vectors with…
In this study an attempt has been made to propose a way to develop new distribution. For this purpose, we need only idea about distribution function. Some important statistical properties of the new distribution like moments, cumulants,…