  The infrared dynamics of a minimally coupled scalar field in de Sitter
spacetime can be described as Brownian motion of a particle in a medium of de
Sitter temperature $T_{DS}=\frac{H}{2\pi}$. The system obeys a
fluctuation-dissipation relation and its equilibrium distribution is
Maxwell-Boltzmann, implying kinetic and potential energies of comparable
magnitudes. The transition to equilibrium is a semi-classical process beyond
the scope of perturbation theory for interacting fields. The stochastic kinetic
energy of the field causes de Sitter spacetime to cool down slowly with a
corresponding decrease of the effective vacuum energy.
