  In the framework of spatially averaged inhomogeneous cosmologies in classical
General Relativity, effective Einstein equations govern the regional and the
global dynamics of averaged scalar variables of cosmological models. A
particular solution may be characterized by a cosmic equation of state. In this
paper it is pointed out that a globally static averaged dust model is
conceivable without employing a compensating cosmological constant. Much in the
spirit of Einstein's original model we discuss consequences for the global, but
also for the regional properties of this cosmology. We then consider the wider
class of globally stationary cosmologies that are conceivable in the presented
framework. All these models are based on exact solutions of the averaged
Einstein equations and provide examples of cosmologies in an out-of-equilibrium
state, which we characterize by an information-theoretical measure. It is shown
that such cosmologies preserve high-magnitude kinematical fluctuations and so
tend to maintain their global properties. The same is true for a
$\Lambda-$driven cosmos in such a state despite of exponential expansion. We
outline relations to inflationary scenarios, and put the Dark Energy problem
into perspective. Here, it is argued, on the grounds of the discussed
cosmologies, that a classical explanation of Dark Energy through backreaction
effects is theoretically conceivable, if the matter-dominated Universe emerged
from a non-perturbative state in the vicinity of the stationary solution. We
also discuss a number of caveats that furnish strong counter arguments in the
framework of structure formation in a perturbed Friedmannian model.
