Comptes Rendus
no. 11
A Note on quantum moment hydrodynamics and the entropy principle
[Une Note sur l'hydrodynamique des moments quantiques et le principe d'entropie]
Pierre Degond1 ; Christian Ringhofer2
1 MIP (UMR CNRS 5640), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 4, France
2 Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA
Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 967-972.

Dans cette Note, nous montrons comment une version non-commutative du principe d'extremalisation de l'entropie permet de construire de nouveaux modèles hydrodynamiques quantiques.

In this Note, we show how a non-commutative version of the entropy extremalization principle allows one to construct new quantum hydrodynamic models.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02595-5
Pierre Degond 1 ; Christian Ringhofer 2

1 MIP (UMR CNRS 5640), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 4, France
2 Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA 
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Pierre Degond; Christian Ringhofer. A Note on quantum moment hydrodynamics and the entropy principle. Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 967-972. doi : 10.1016/S1631-073X(02)02595-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02595-5/

[1] P. Degond, C. Ringhofer, Quantum moment hydrodynamics and the entropy principle, Manuscript

[2] D. Ferry; H. Grubin Modelling of quantum transport in semiconductor devices, Solid State Phys, Volume 49 (1995), pp. 283-448

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[4] C. Gardner; C. Ringhofer The smooth quantum potential for the hydrodynamic model, Phys. Rev. E, Volume 53 (1996), pp. 157-167

[5] C. Gardner; C. Ringhofer The Chapman–Enskog expansion and the quantum hydrodynamic model for semiconductor devices, VLSI Design, Volume 10 (2000), pp. 415-435

[6] I. Gasser; P. Markowich; C. Ringhofer Closure conditions for classical and quantum moment hierarchies in the small temperature limit, Transport Theory Statist. Phys, Volume 25 (1996), pp. 409-423

[7] H. Grubin; J. Krekovski Quantum moment balance equations and resonant tunneling structures, Solid State Electron, Volume 32 (1989), pp. 1071-1075

[8] C.D. Levermore Moment closure hierarchies for kinetic theories, J. Statist. Phys, Volume 83 (1996), pp. 1021-1065

[9] R. Luzzi (arXiv: v2 11 Sep 1999) | arXiv

[10] V.G. Morozov; G. Röpke Zubarev's method of a nonequilibrium statistical operator and some challenges in the theory of irreversible processes, Condensed Matter Phys, Volume 1 (1998), pp. 673-686

[11] I. Muller; T. Ruggeri Rational Extended Thermodynamics, Springer Tracts Nat. Philos, 37, Springer, 1998

[12] M.A. Shubin Pseudodifferential Operators and Spectral Theory, Springer, 1980

[13] D.N. Zubarev; V.G. Morozov; G. Röpke Statistical Mechanics of Nonequilibrium Processes, Vol. 1, Basic Concepts, Kinetic Theory, Akademie-Verlag, Berlin, 1996

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