Comptes Rendus
no. 5-6
Temporal ordering of nonequilibrium fluctuations as a corollary of the second law of thermodynamics
[Ordonnancement temporel des fluctuations de non-équilibre comme corollaire de la seconde loi de la thermodynamique]
Pierre Gaspard1
1 Center for Nonlinear Phenomena and Complex Systems, Université libre de Bruxelles, code postal 231, campus Plaine, B-1050 Brussels, Belgium
Comptes Rendus. Physique, Work, dissipation, and fluctuations in nonequilibrium physics, Volume 8 (2007) no. 5-6, pp. 598-608.

Dans les états stationnaires de non-équilibre, les probabilités des chemins renversés dans le temps diffèrent en général des probabilités des chemins et elles décroissent à des taux donnés par les entropies par unité de temps, respectivement réverse et standard. Ces quantités caractérisent le désordre temporel des chemins renversés dans le temps et des chemins eux-mêmes. La différence entre ces quantités donne la production d'entropie thermodynamique en unités de la constante de Boltzmann. Hors d'équilibre, il ressort que le désordre temporel des chemins renversés dans le temps est plus grand que le désordre temporel des chemins eux-mêmes. Ainsi, un théorème est obtenu selon lequel l'ordre temporel des chemins est plus grand que pour les chemins renversés dans le temps. Le désordre temporel ou hasard dynamique des chemins et des chemins réverses ont des propriétés de grandes déviations directement reliées à la production d'entropie thermodynamique.

In nonequilibrium steady states, the probabilities of the time-reversed paths differ in general from the path probabilities and they decrease at different rates given, respectively, by the time-reversed and standard entropies per unit time. These quantities characterize temporal disorder in the time-reversed paths and the paths themselves. The difference between these quantities gives the thermodynamic entropy production in units of Boltzmann's constant. Out of equilibrium, the temporal disorder of the time-reversed paths turns out to be larger than the temporal disorder of the paths themselves. In this way, a theorem is obtained according to which the temporal order of the paths is greater than for the time-reversed paths. The temporal disorder or dynamical randomness of the paths and their time-reversal have large-deviation properties directly connected to the thermodynamic entropy production.

Reçu le :
Publié le :
DOI : 10.1016/j.crhy.2007.05.002
Keywords: Thermodynamic entropy production, Dynamical randomness, Entropy per unit time, Time reversal
Mots-clés : Production d'entropie thermodynamique, Hasard dynamique, Entropie par unité de temps, Renversement du temps

Pierre Gaspard 1

1 Center for Nonlinear Phenomena and Complex Systems, Université libre de Bruxelles, code postal 231, campus Plaine, B-1050 Brussels, Belgium 
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Pierre Gaspard. Temporal ordering of nonequilibrium fluctuations as a corollary of the second law of thermodynamics. Comptes Rendus. Physique, Work, dissipation, and fluctuations in nonequilibrium physics, Volume 8 (2007) no. 5-6, pp. 598-608. doi : 10.1016/j.crhy.2007.05.002. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2007.05.002/

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