Abstract: We consider the local physics of an open quantum system embedded in an expanding three-dimensional space 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 1/4 const, the background fields act as a physical heat bath with temperature TdS 1/4 h/2z. The energy density of this bath obeys the Stefan-Boltzmann law pdS proportional to h4. 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.