Comptes Rendus
no. 5-6
Relativistic fluctuation theorems
[Théorèmes de fluctuations relativistes]
Axel Fingerle1
1 Max Planck Institute for Dynamics and Self-Organization, Bunsenstr. 10, 37073 Göttingen, Germany
Comptes Rendus. Physique, Work, dissipation, and fluctuations in nonequilibrium physics, Volume 8 (2007) no. 5-6, pp. 696-713.

Pour révéler comment la physique de non-équilibre et la théorie relativiste se combinent, cet article étudie le mouvement brownien relativiste sous l'effet de l'expansion cosmique. Deux théorèmes de fluctuations sont présentés et démontrés pour l'entropie Δs qui est localement produite dans cette situation de non-équilibre extrême. Le premier, 〈e−Δs〉=1, est une généralisation du second principe de la thermodynamique qui reste valable aux énergies relativistes des particules et pour de hauts taux d'expansion cosmique. De cette relation, il suit que la probabilité d'observer une réduction locale de l'entropie est exponentiellement petite même si l'univers venait à se recomprimer. Dans le cas spécial de l'univers d'Einstein–de Sitter, une relation supplémentaire, 〈e−Δs−Δh〉=1, est dérivée qui est valable conjointement avec la première relation et où Δh est proportionnel à la constante de Hubble. De plus, il est montré que les théorèmes de fluctuations fournissent un critère physique pour résoudre le dilemme connu de la discrétisation dans le mouvement brownien en relativité restreinte. Des exemples explicites et une méthode générale pour le calcul des fluctuations non-gaussiennes d'entropie sont donnés.

To reveal how nonequilibrium physics and relativity theory intertwine, this article studies relativistic Brownian motion under cosmic expansion. Two fluctuation theorems for the entropy Δs, which is locally produced in this extreme nonequilibrium situation, are presented and proven. The first, 〈e−Δs〉=1, is a generalization of the second law of thermodynamics, that remains valid at relativistic particle energies and under high cosmic expansion rates. From this relation follows that the probability of observing a local reduction of entropy is exponentially small even if the universe was to recollapse. For the special case of the Einstein–de Sitter universe, an additional relation, 〈e−Δs−Δh〉=1, is derived which holds simultaneously with the first relation and where Δh is proportional to the Hubble constant. Furthermore, the fluctuation theorems are shown to provide a physical criterion to resolve the known discretization dilemma arising in special-relativistic Brownian motion. Explicit examples and a general method for the computation of non-Gaussian entropy fluctuations are provided.

Reçu le :
Publié le :
DOI : 10.1016/j.crhy.2007.05.015
Keywords: Fluctuation theorems, Nonequilibrium physics
Mots-clés : Théorèmes de fluctuations, Physique de non-équilibre

Axel Fingerle 1

1 Max Planck Institute for Dynamics and Self-Organization, Bunsenstr. 10, 37073 Göttingen, Germany 
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Axel Fingerle. Relativistic fluctuation theorems. Comptes Rendus. Physique, Work, dissipation, and fluctuations in nonequilibrium physics, Volume 8 (2007) no. 5-6, pp. 696-713. doi : 10.1016/j.crhy.2007.05.015. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2007.05.015/

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