Relativistic fluctuation theorems

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 Δ s, which is locally produced in this extreme nonequilibrium situation, are presented and proven. The first, 〈 e − Δ s 〉 = 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 − Δ s − Δ h 〉 = 1 , is derived which holds simultaneously with the first relation and where Δ h 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).