  In this paper, an open quantum system theory for spinfoams is developed. This
new formalism aims at deriving an effective Lindblad equation to compute the
reduced dynamics of a quantum gravitational field. The system parameters are
determined from numerical ab initio calculations, based on the spinfoam
formalism. This theoretical proposal is illustrated by means of examples. The
decoherence effect can induce the relaxation of the quantum gravitational state
toward a sate of a small area. This is analogue to the well-known Purcell
relaxation of QED, for which the qubits are replaced by the spin-network
representation of the gravitational field. Some thermodynamic properties of
these systems are computed, and several issues with the thermal time hypothesis
are underlined. Moreover, the results suggest that further approximations can
be performed to study reduced dynamics of quantum space-time.
