  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.
