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Entropic approximation in kinetic theory

Jacques Schneider (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys. 83 (1996) 1021–1065] and based on an entropy minimization principle under moment constraints. We prove in particular a global...

Entropic approximation in kinetic theory

Jacques Schneider (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys.83 (1996) 1021–1065] and based on an entropy minimization principle under moment constraints. We prove in particular...

Entropy maximisation problem for quantum relativistic particles

Miguel Escobedo, Stéphane Mischler, Manuel A. Valle (2005)

Bulletin de la Société Mathématique de France

The entropy of an ideal gas, both in the case of classical and quantum particles, is maximised when the number particle density, linear momentum and energy are fixed. The dispersion law energy to momentum is chosen as linear or quadratic, corresponding to non-relativistic or relativistic behaviour.

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