Related papers: Choi-Davis-Jensen's inequality without convexity
In this paper, we establish some integral inequalities for functions whose second derivatives in absolute value are ({\alpha},m)- convex.
Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a.…
Most quantum divergences derive their structure from classical f-divergences or Renyi-type constructions, a dependence that obscures several quantum geometric effects. We introduce a quantum relative-alpha-entropy that extends Umegaki's…
Tsallis relative operator entropy is defined and then its properties are given. Shannon inequality and its reverse one in Hilbert space operators derived by T.Furuta \cite{Fu:par} are extended in terms of the parameter of the Tsallis…
It is demonstrated that, making minimal changes in ordinary quantum mechanics, a reasonable irreversible quantum mechanics can be obtained. This theory has a more general spectral decompositions, with eigenvectors corresponding to unstable…
Purely multiplicative comparisons of quantum relative entropy are desirable but challenging to prove. We show such comparisons for relative entropies between comparable densities, including the relative entropy of a density with respect to…
We establish several optimal moment comparison inequalities (Khinchin-type inequalities) for weighted sums of independent identically distributed symmetric discrete random variables which are uniform on sets of consecutive integers.…
By imposing special compatible similarity constraints on a class of integrable partial $q$-difference equations of KdV-type we derive a hierarchy of second-degree ordinary $q$-difference equations. The lowest (non-trivial) member of this…
We prove the Shannon's inequality on non-collapsing $\mathsf{RCD}(0,N)$ spaces. In the proof, we use the characterization of the $\mathsf{EVI}_{0,N}$-gradient flow of the relative entropy and the infinitesimal behavior of the heat kernel.…
In the past over two decades, very fruitful results have been obtained in information theory in the study of the Shannon entropy. This study has led to the discovery of a new class of constraints on the Shannon entropy called…
In this paper we establish for the first time local semiconvexity estimates for fully nonlinear equations and for obstacle problems driven by integro-differential operators with general kernels. Our proof is based on the Bernstein…
We introduce a new class of (not necessarily convex) bodies and show, among other things, that these bodies provide yet another link between convex geometric analysis and information theory. Namely, they give geometric interpretations of…
We give new upper and lower bounds on the concavity of quantum entropy. Comparisons are given with other results in the literature.
We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy…
In this paper, we establish noncommutative Burkholder inequalities with asymmetric diagonals in symmetric operator spaces. Our proof mainly relies on a new complex interpolation result on asymmetric vector valued spaces and a duality…
We show that, in the periodic homogenization of uniformly elliptic Hamilton-Jacobi equations in any dimension, the effective Hamiltonian does not necessarily inherit the quasiconvexity property (in the momentum variables) of the original…
We study the mean values sets of the second order divergence form elliptic operator with principal coefficients defined as $$a^{ij}_k(x):= \begin{cases} \alpha_k \delta^{ij}(x) &x_n>0 \beta_k \delta^{ij}(x) &x_n<0. \end{cases}$$ In…
It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a…
In this paper, we established some new inequalities via s-convex and s-concave functions.
We will establish the Caffarelli-Kohn-Nirenberg type inequalities with non-doubling weights being permitted. The classical Caffarelli-Kohn-Nirenberg type inequalities are categorized into non-critical and critical cases, and it is known…