  Statistical equilibrium configurations are important in the physics of
macroscopic systems with a large number of constituent degrees of freedom. They
are expected to be crucial also in discrete quantum gravity, where dynamical
spacetime should emerge from the collective physics of the underlying quantum
gravitational degrees of freedom. However, defining statistical equilibrium in
a background independent system is a challenging open issue, mainly due to the
absence of absolute notions of time and energy. This is especially so in
non-perturbative quantum gravity frameworks that are devoid of usual space and
time structures. In this thesis, we investigate aspects of a generalisation of
statistical equilibrium, specifically Gibbs states, suitable for background
independent systems. We emphasise on an information theoretic characterisation
based on the maximum entropy principle. Subsequently, we explore the resultant
generalised Gibbs states in a discrete quantum gravitational system composed of
many candidate quanta of geometry, utilising their field theoretic formulation
of group field theory and various many-body techniques. We construct several
concrete examples of quantum gravitational generalised Gibbs states. We further
develop inequivalent thermal representations based on entangled, two-mode
squeezed, thermofield double vacua, induced by a class of generalised Gibbs
states. In these representations, we define a class of thermal condensates
which encode statistical fluctuations in a given observable, e.g. volume of the
quantum geometry. We apply these states in the condensate cosmology programme
of group field theory to study a relational effective cosmological dynamics
extracted from a class of free models, for homogeneous and isotropic
spacetimes. We find the correct classical limit of Friedmann equations at late
times, with a bounce and accelerated expansion at early times.
