Related papers: Some inequalities on generalized entropies
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional…
In recent years, learning for neural networks can be viewed as optimization in the space of probability measures. To obtain the exponential convergence to the optimizer, the regularizing term based on Shannon entropy plays an important…
In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp…
We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…
In this paper we derived a 6N dimensional non-homogeneous evolution equation of Tsallis non-equilibrium entropy; presented a formula for entropy production rate (i.e. the law of entropy increase) for Tsallis entropy only when its index q>0,…
In this paper we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents as well as inequalities with certain polynomial exponents. Also, we establish intervals in which…
Recently, a new measure of information called extropy has been introduced by Lad, Sanfilippo and Agr\`o as the dual version of Shannon entropy. In the literature, Tsallis introduced a measure for a discrete random variable, named Tsallis…
We determine a general link between two different solutions of the MaxEnt variational problem, namely, the ones that correspond to using either Shannon's or Tsallis' entropies in the concomitant variational problem. It is shown that the two…
We present our view in a standing debate about the definition and meaning of power-law entropies for continuous systems. Our suggestion is that such arguments should take into account the generalized operations of addition and…
In this paper, we study the further improvements of the reverse Young and Heinz inequalities for the wider range of $v$, namely $v\in \mathbb{R}$. These modified inequalities are used to establish corresponding operator inequalities on a…
In this paper, we study entropic uncertainty relations on a finite-dimensional Hilbert space and provide several tighter bounds for multi-measurements, with some of them also valid for R\'{e}nyi and Tsallis entropies besides the Shannon…
Here we explain how C. Tsallis' reply (Entropy 2021, 23(5), 630) fails to respond to points raised in (Entropy 2020, 22(10), 1110) and introduces further inconsistencies on the origin of black hole entropy. In his reply, Tsallis argues that…
Some inequalities for different types of convexity are established.
A family of nonlinear ordinary differential equations with arbitrary order is obtained by using nonextensive concepts related to the Tsallis entropy. Applications of these equations are given here. In particular, a connection between…
We propose a generalization of the quantum entropy power inequality involving conditional entropies. For the special case of Gaussian states, we give a proof based on perturbation theory for symplectic spectra. We discuss some implications…
A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex…
An extension of the entropy power inequality to the form $N_r^\alpha(X+Y) \geq N_r^\alpha(X) + N_r^\alpha(Y)$ with arbitrary independent summands $X$ and $Y$ in $\mathbb{R}^n$ is obtained for the R\'enyi entropy and powers $\alpha \geq…
Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent…
We give new upper and lower bounds on the concavity of quantum entropy. Comparisons are given with other results in the literature.