Comptes Rendus
no. 5-6
Cumulants and large deviations of the current through non-equilibrium steady states
[Cumulants et grandes déviations du courant dans des états stationnaires hors équilibre]
Thierry Bodineau1 ; Bernard Derrida2 
1 Universités Paris VI & VII, Laboratoire de probabilités et modèles aléatoires, CNRS-UMR 7599, 4, place Jussieu, case 188, 75252 Paris cedex 05, France
2 Laboratoire de physique statistique, École normale supérieure, CNRS-UMR 8550, 24, rue Lhomond, 75231 Paris cedex 05, France
Comptes Rendus. Physique, Work, dissipation, and fluctuations in nonequilibrium physics, Volume 8 (2007) no. 5-6, pp. 540-555.

En généralisant la relation de bilan détaillé à des systèmes maintenus hors équilibre par contact avec deux réservoirs à des températures ou à des densités différentes, nous retrouvons le théorème de fluctuations pour la fonction de grandes déviations du courant. Pour de grands systèmes diffusifs, nous montrons comment la fonction de grandes déviations du courant peut être calculée simplement à l'aide d'un principe d'additivité. La validité de ce principe d'additivité et l'existence de transitions de phase sont discutées dans le cadre d'une théorie des fluctuations à l'échelle macroscopique.

Using a generalisation of detailed balance for systems maintained out of equilibrium by contact with 2 reservoirs at unequal temperatures or at unequal densities, one can recover the fluctuation theorem for the large deviation function of the current. For large diffusive systems, we show how the large deviation function of the current can be computed using a simple additivity principle. The validity of this additivity principle and the occurrence of phase transitions are discussed in the framework of the macroscopic fluctuation theory.

Reçu le :
Publié le :
DOI : 10.1016/j.crhy.2007.04.014
Keywords: Non-equilibrium steady state, Current fluctuations, Generalized detailed balance
Mots-clés : Systèmes hors équilibre, Fluctuations du courant, Bilan détaillé généralisé

Thierry Bodineau 1 ; Bernard Derrida 2

1 Universités Paris VI & VII, Laboratoire de probabilités et modèles aléatoires, CNRS-UMR 7599, 4, place Jussieu, case 188, 75252 Paris cedex 05, France
2 Laboratoire de physique statistique, École normale supérieure, CNRS-UMR 8550, 24, rue Lhomond, 75231 Paris cedex 05, France 
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Thierry Bodineau; Bernard Derrida. Cumulants and large deviations of the current through non-equilibrium steady states. Comptes Rendus. Physique, Work, dissipation, and fluctuations in nonequilibrium physics, Volume 8 (2007) no. 5-6, pp. 540-555. doi : 10.1016/j.crhy.2007.04.014. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2007.04.014/

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⁎ We thank H. Spohn for useful suggestions. We acknowledge the support of the ACI-NIM 168 Transport Hors Equilibre of the Ministère de l'Education Nationale, France.

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