Related papers: Representation formula for the entropy and functio…

We show that linear inequalities for entropies have a natural geometric interpretation in terms of Hausdorff and packing dimensions, using the point-to-set principle and known results about inequalities for complexities, entropies and the…

On the basis of a manifestly covariant formalism of non-relativistic quantum mechanics in general coordinate systems, proposed by us recently, we derive general expressions for inertial forces. The results enable us further to discuss, and…

The aim of this note is to connect a reversed form of the Gross logarithmic Sobolev inequality with the Gaussian maximum of Shannon's entropy power. There is thus a complete parallel with the well-known link between logarithmic Sobolev…

We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving…

We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is…

We present a simple proof of the entropy-power inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse inequality involving a conditional differential…

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.…

We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosaki's formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched…

We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional…

Generalized versions of the entropic (Hirschman-Beckner) and support (Elad-Bruckstein) uncertainty principle are presented for frames representations. Moreover, a sharpened version of the support inequality has been obtained by introducing…

This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…

Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…

We establish the existence and compactness of global martingale entropy solutions with finite relative-energy for the stochastically forced system of isentropic Euler equations governed by a general pressure law. To achieve these, a…

In this paper we study the geodesic flow for a particular class of Riemannian non-compact manifolds with variable pinched negative sectional curvature. For a sequence of invariant measures we are able to prove results relating the loss of…

Within the framework of Gaussian equivalent representation method a new procedure of obtaining equations of state for simple liquids is discussed in some technical details. The developed approach permits one to compute partition and…

We review the properties of the quantum relative entropy function and discuss its application to problems of classical and quantum information transfer and to quantum data compression. We then outline further uses of relative entropy to…

A formulation of the density functional theory is constructed on the foundations of entropic inference. The theory is introduced as an application of maximum entropy for inhomogeneous fluids in thermal equilibrium. It is shown that entropic…

Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…

We prove existence of the largest and the smallest entropy solutions to the Cauchy problem for a nonlinear degenerate anisotropic parabolic equation. Applying this result, we establish the comparison principle in the case when at least one…

We explore a well-known integral representation of the logarithmic function, and demonstrate its usefulness in obtaining compact, easily-computable exact formulas for quantities that involve expectations and higher moments of the logarithm…