Centered numerical fluxes can be constructed for compressible Euler equations which preserve kinetic energy in the semi-discrete finite volume scheme. The essential feature is that the momentum flux should be of the form f m j+ 1 2 = p̃j+ 1 2 +uj+ 1 2 f ρ j+ 2 where uj+ 2 = (uj+uj+1)/2 and p̃j+ 1 2 , f ρ j+ 1 2 are any consistent approximations to the pressure and the mass flux. This scheme thus ...

There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of e...

New one-leg multistep time discretizations of nonlinear evolution equations are investigated. The main features of the scheme are the preservation of the nonnegativity and the entropy-dissipation structure of the diffusive equations. The key ideas are to combine Dahlquist’s G-stability theory with entropy-dissipation methods and to introduce a nonlinear transformation of variables which provide...

The concept of entropy plays a major part in communication theory. The Shannon entropy is a measure of uncertainty with respect to a priori probability distribution. In algorithmic information theory the information content of a message is measured in terms of the size in bits of the smallest program for computing that message. This paper discusses the classical entropy and entropy rate for dis...

We introduce discrete-time linear control systems on connected Lie groups and present an upper bound for the outer invariance entropy of admissible pairs ( K , Q ). If stable subgroup uncontrolled system is closed has positive measure a left invariant Haar measure, coincides with entropy.

We establish forward and backward relations between entropy satisfying BGK relaxation models such as those introduced previously by the author and the rst order ux vector splitting numerical methods for general systems of conservation laws. Classically, to a kinetic BGK model that is compatible with some family of entropies we can associate an entropy ux vector splitting. We prove that the conv...

Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its analytic properties relative to some reasonable topology. A canonical choice of a topology is that of the norm of total variation as it immediately arises with th...

We introduce a fully discrete (in both space and time) scheme for the numerical approximation of diffusive-dispersive hyperbolic conservation laws in one-space dimension. This scheme extends an approach by LeFloch and Rohde [4]: it satisfies a cell entropy inequality and, as a consequence, the space integral of the entropy is a decreasing functionof time.This is an important stability property,...

In this paper we use information-theoretic measures to provide a theory and tools to analyze the flow of information from a discrete, multivariate source of information X to a discrete, multivariate sink of information Y joined by a distribution PXY . The first contribution is a decomposition of the maximal potential entropy of (X,Y ) that we call a balance equation, that can also be split into...

Localization systems are increasingly valuable, but their location estimates are only useful when the uncertainty of the estimate is known. This uncertainty is currently calculated as the location error given a ground truth, which is then used as a static measure in sometimes very different environments. In contrast, we propose the use of the conditional entropy of a posterior probability distr...