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Comptes Rendus Physique
Volume 8, n° 5-6
pages 696-713 (juin 2007)
Doi : 10.1016/j.crhy.2007.05.015
Received : 2 April 2007 ; 
Relativistic fluctuation theorems
Théorèmes de fluctuations relativistes
 

Axel Fingerle
Max Planck Institute for Dynamics and Self-Organization, Bunsenstr. 10, 37073 Göttingen, Germany 

Abstract

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,  , 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,  , 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. To cite this article: A. Fingerle, C. R. Physique 8 (2007).

The full text of this article is available in PDF format.
Résumé

Pour révéler comment la physique de non-équilibre et la théorie relativiste se combinent, cet article étudie le mouvement brownien relativiste sous lʼeffet de lʼexpansion cosmique. Deux théorèmes de fluctuations sont présentés et démontrés pour lʼentropie δs qui est localement produite dans cette situation de non-équilibre extrême. Le premier,  , est une généralisation du second principe de la thermodynamique qui reste valable aux énergies relativistes des particules et pour de hauts taux dʼexpansion cosmique. De cette relation, il suit que la probabilité dʼobserver une réduction locale de lʼentropie est exponentiellement petite même si lʼunivers venait à se recomprimer. Dans le cas spécial de lʼunivers dʼEinstein-de Sitter, une relation supplémentaire,  , 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 dʼentropie sont donnés. Pour citer cet article : A. Fingerle, C. R. Physique 8 (2007).

The full text of this article is available in PDF format.

Keywords : Fluctuation theorems, Nonequilibrium physics

Mots-clés : Théorèmes de fluctuations, Physique de non-équilibre




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