Relativistic Fluctuation Theorems: Theory and explicit examples

TL;DR

This paper develops and proves relativistic fluctuation theorems for entropy production in cosmic expansion scenarios, extending nonequilibrium thermodynamics into relativistic and cosmological contexts with explicit examples.

Contribution

It introduces new fluctuation theorems applicable to relativistic Brownian motion in expanding universes, including explicit formulas and a method for non-Gaussian entropy fluctuation calculations.

Findings

The fluctuation theorem <exp(-ds)>=1 generalizes the second law to relativistic regimes.

In the Einstein-de Sitter universe, <exp(-ds-dh)>=1 relates entropy fluctuations to cosmic expansion.

The theorems provide criteria to resolve discretization issues in relativistic Brownian motion.

Abstract

To reveal how nonequilibrium physics and relativity theory intertwine, this articles studies relativistic Brownian motion under cosmic expansion. Two fluctuation theorems for the entropy ds, which is locally produced in this extreme nonequilibrium situation, are presented and proven. The first, <exp(-ds)>=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 to observe 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, <exp(-ds-dh)>=1, is derived which holds simultaneously with the first relation and where dh 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.