  Dense Rydberg gases are out-of-equilibrium systems where strong
density-density interactions give rise to effective kinetic constraints. They
cause dynamic arrest associated with highly-constrained many-body
configurations, leading to slow relaxation and glassy behavior. Multi-component
Rydberg gases feature additional long-range interactions such as
excitation-exchange. These are analogous to particle swaps used to artificially
accelerate relaxation in simulations of atomistic models of classical glass
formers. In Rydberg gases, however, swaps are real physical processes, which
provide dynamical shortcuts to relaxation. They permit the accelerated approach
to stationarity in experiment and at the same time have an impact on the
non-equilibrium stationary state. In particular their interplay with radiative
decay processes amplifies irreversibility of the dynamics, an effect which we
quantify via the entropy production at stationarity. Our work highlights an
intriguing analogy between real dynamical processes in Rydberg gases and
artificial dynamics underlying advanced Monte Carlo methods. Moreover, it
delivers a quantitative characterization of the dramatic effect swaps have on
the structure and dynamics of their stationary state.
