The problem considered here is motivated by a work B. Nachtergaele and H.T. Yau where the Euler equations of fluid dynamics are derived from manybody quantum mechanics, see [10]. A crucial concept in their that local Gibbs states, which statistical equilibria with prescribed particle, current, energy densities at each point space (here R d , $\ge$ 1). They assume such states exist, show if syst...

In the framework of a two-moment photo-hydrodynamic modelling of radiation transport, we introduce a concept for the determination of effective radiation transport coefficients based on the minimization of the local entropy production rate of radiation and matter. The method provides the nonequilibrium photon distribution from which the effective absorption coefficients and the variable Eddingt...

In this paper, we analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalty function in place of the usual quadratic. We also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it...

Isothermal quantum hydrodynamic equations of order O(~) using the quantum entropy minimization method recently developed by Degond and Ringhofer are derived. The equations have the form of the usual quantum hydrodynamic model including a correction term of order O(~) which involves the vorticity. If the initial vorticity is of order O(~), the standard model is obtained up to order O(~). The der...

Kullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras’ theorem. And hence, this property is referred to as Pythagoras’ theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical ...

There are many techniques of image enhancement. Their parameters are traditionally tuned by maximization of SNR criterion, which is unfortunately based on the knowledge of an ideal image. Our approach is based on Hartley entropy, its estimation, and differentiation. Resulting gradient of entropy is estimated without knowledge of ideal images, and it is a subject of minimization. Both SNR maximi...

In the modeling of solids the free energy, the energy, and the entropy play a central role. We show that the free entropy, which is defined as the negative of the free energy divided by the temperature, is similarly important. The derivatives of the free energy are suitable thermodynamical driving forces for reversible (i.e. Hamiltonian) parts of the dynamics, while for the dissipative parts th...

We study minimization of a parametric family of relative entropies, termed relative α-entropies (denoted Iα(P,Q)). These arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (KullbackLeibler divergence). Just like relati...