  When atoms are excited to high-lying Rydberg states they interact strongly
with dipolar forces. The resulting state-dependent level shifts allow to study
many-body systems displaying intriguing nonequilibrium phenomena, such as
constrained spin systems, and are at the heart of numerous technological
applications, e.g., in quantum simulation and computation platforms. Here, we
show that these interactions have also a significant impact on dissipative
effects caused by the inevitable coupling of Rydberg atoms to the surrounding
electromagnetic field. We demonstrate that their presence modifies the
frequency of the photons emitted from the Rydberg atoms, making it dependent on
the local neighborhood of the emitting atom. Interactions among Rydberg atoms
thus turn spontaneous emission into a many-body process which manifests, in a
thermodynamically consistent Markovian setting, in the emergence of collective
jump operators in the quantum master equation governing the dynamics. We
discuss how this collective dissipation - stemming from a mechanism different
from the much studied super- and sub-radiance - accelerates decoherence and
affects dissipative phase transitions in Rydberg ensembles.
