Related papers: Entropy-power inequality for weighted entropy
We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an…
In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincar\'{e} inequalities, general Beckner inequalities...). We also discuss the…
Equivalencies of many basic elementary inequalities are given
In this paper, we obtain non-symmetric and symmetric versions of the classical Heisenberg-Pauli-Weyl uncertainty principle in Lebesgue spaces with power weights.
We consider the entropic force in matrix theory. We find the gravity in bulk can be emergent from the entropic force.
The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…
It is commonplace, in the literature, to find that the Bekenstein-Hawking entropy has been endowed with having an explicit statistical interpretation. In the following essay, we discuss why such a viewpoint warrants a certain degree of…
The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some…
We provide a generalized definition of polygamy relations for any quantum correlation measures. Instead of the usual polygamy inequality, a polygamy relation with equality is given by introducing the polygamy weight. From the polygamy…
We derive again the upper entropy bound for a charged object by employing thermodynamics of the Kerr-Newman black hole linearised with respect to its electric charge
This thesis discusses the possibility of uncertainty relations for space and energy given a state of fixed entropy. In particular, it discusses the results in the paper of Dam/Nguyen. There, the authors propose a lower bound for the mixed…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
We obtain formulas for the coefficients of positive and negative powers of a partial theta function.
In this paper, we prove some inequalities for the differences and ratios of the beta function.
We obtain sharp inequalities for the k-plane transform, the "j-plane to k-plane" transform, and the corresponding dual transforms, acting on $L^p$ spaces with a radial power weight. The operator norms are explicitly evaluated. Some…
In previous works, entropic gravity and ungravity have been considered as possible solutions to the dark energy and dark matter problems. To test the viability of these models, modifications to planetary orbits are calculated for ungravity…
Discussion of ``EQUI-energy sampler'' by Kou, Zhou and Wong [math.ST/0507080]
Discussion of ``EQUI-energy sampler'' by Kou, Zhou and Wong [math.ST/0507080]
This paper is concerned with certain invariant random processes (called factors of IID) on infinite trees. Given such a process, one can assign entropies to different finite subgraphs of the tree. There are linear inequalities between these…
We give a refined Young inequality which generalizes the inequality by Zou--Jiang. We also show the upper bound for the logarithmic mean by the use of the weighted geometric mean and the weighted arithmetic mean. Furthermore, we show some…