  A variety of quantum gravity models (including spin foams) can be described
using a path integral formulation. A path integral has a well-known statistical
mechanical interpretation in connection with a canonical ensemble. In this
sense, a path integral describes the thermodynamic equilibrium of a local
system in a thermal bath. This interpretation is in contrast to solutions of
Einstein's Equations which depart from local thermodynamical equilibrium (one
example is shown explicitly). For this reason, we examine an extension of the
path integral model to a (locally) non-equilibrium description. As a
non-equilibrium description, we propose to use a global microcanonical ensemble
with constraints. The constraints reduce the set of admissible microscopic
states to be consistent with the macroscopic geometry. We also analyse the
relation between the microcanonical description and a statistical approach not
based on dynamical assumptions which has been proposed recently. This analysis
is of interest for the test of consistency of the non-equilibrium description
with general relativity and quantum field theory.
