[Théorème de fluctuations quantiques : peut-on aller du micro au méso ?]
Des extensions quantiques du théorème de fluctuations (TF) de Gallavotti et Cohen pour la production d'entropie ont été discutées par plusieurs auteurs. Il y a une séparation pratique entre les formes microscopiques du TF et les formes mésoscopiques (c'est-à-dire non purement hamiltoniennes) pour les systèmes ouverts. Dans un schéma microscopique, il est facile d'énoncer et de démontrer le TF. Dans un schéma mésoscopique, il est difficile d'identifier les fluctuations de la production d'entropie. (Cette difficulté est absente dans le cas classique.) Nous discutons un modèle mésoscopique particulier : une équation maîtresse de Lindblad pour laquelle nous énonçons le TF et, ce qui est plus important, nous le connectons rigoureusement avec le TF microscopique. Nous remarquons aussi que le TF est satisfait par la formule de Lesovik–Levitov pour la statistique du transport de charges.
Quantum extensions of the Gallavotti–Cohen fluctuation theorem (FT) for the entropy production have been discussed by several authors. There is a practical gap between microscopic forms of FT and mesoscopic (i.e. not purely Hamiltonian) forms for open systems. In a microscopic setup, it is easy to state and to prove FT. In a mesoscopic setup, it is difficult to identify fluctuations of the entropy production. (This difficulty is absent in the classical case.) We discuss a particular mesoscopic model: a Lindblad master equation, in which we state FT and, more importantly, connect it rigorously with the underlying microscopic FT. We also remark that FT is satisfied by the Lesovik–Levitov formula for statistics of charge transport.
Publié le :
Mot clés : Théorème de fluctuations quantiques, Production d'entropie
Wojciech De Roeck 1, 2
@article{CRPHYS_2007__8_5-6_674_0,
author = {Wojciech De Roeck},
title = {Quantum fluctuation theorem: can we go from micro to meso?},
journal = {Comptes Rendus. Physique},
pages = {674--683},
publisher = {Elsevier},
volume = {8},
number = {5-6},
year = {2007},
doi = {10.1016/j.crhy.2007.05.014},
language = {en},
}
Wojciech De Roeck. Quantum fluctuation theorem: can we go from micro to meso?. Comptes Rendus. Physique, Volume 8 (2007) no. 5-6, pp. 674-683. doi : 10.1016/j.crhy.2007.05.014. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2007.05.014/
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