Entropy inequality and hydrodynamic limits for the Boltzmann equation

Boltzmann brought a fundamental contribution to the understanding of the notion of entropy, by giving a microscopic formulation of the second principle of thermodynamics. His ingenious idea, motivated by the works of his contemporaries on the atomic nature of matter, consists of describing gases as...

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Published inPhilosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 371; no. 2005; pp. 1 - 17
Main Author Saint-Raymond, Laure
Format Journal Article
LanguageEnglish
Published The Royal Society 28.12.2013
Subjects
Boltzmann equation
Entropy
Euler equations
Hydrodynamics
Income inequality
Kinetics
Mathematics
Particle velocity
Thermodynamic equilibrium
Velocity
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Summary:Boltzmann brought a fundamental contribution to the understanding of the notion of entropy, by giving a microscopic formulation of the second principle of thermodynamics. His ingenious idea, motivated by the works of his contemporaries on the atomic nature of matter, consists of describing gases as huge systems of identical and indistinguishable elementary particles. The state of a gas can therefore be described in a statistical way. The evolution, which introduces couplings, loses part of the information, which is expressed by the decay of the so-called mathematical entropy (the opposite of physical entropy!).
ISSN:1364-503X
1471-2962