  We consider the local physics of an open quantum system embedded in an
expanding three-dimensional space $\mathbf x$, evolving in cosmological time
$t$, weakly coupled to a massless quantum field. We derive the corresponding
Markovian master equation for the system's nonunitary evolution and show that,
for a de Sitter space with Hubble parameter $h = $ const., the background
fields act as a physical heat bath with temperature $T_{\rm dS} = h / 2 \pi$.
The energy density of this bath obeys the Stefan-Boltzmann law $\rho_{\rm dS}
\propto h^4$. We comment on how these results clarify the thermodynamics of de
Sitter space and support previous arguments for its instability in the
infrared. The cosmological implications are considered in an accompanying
letter.
