  We develop further our fibre bundle construct of non-commutative space-time
on a Minkowski base space. We assume space-time is non-commutative due to the
existence of additional non-commutative algebraic structure at each point x of
space-time, forming a quantum operator 'fibre algebra' A(x). This structure
then corresponds to the single fibre of a fibre bundle. A gauge group acts on
each fibre algebra locally, while a 'section' through this bundle is then a
quantum field of the form {A(x); x in M} with M the underlying space-time
manifold. In addition, we assume a local algebra O(D) corresponding to the
algebra of sections of such a principal fibre bundle with base space a finite
and bounded subset of space-time, D. The algebraic operations of addition and
multiplication are assumed defined fibrewise for this algebra of sections. We
characterise 'ergodic' extremal quantum states of the fibre algebra invariant
under the subgroup T of local translations of space-time of the Poincare group
P in terms of a non-commutative extension of entropy applied to the subgroup T.
We also characterise the existence of T- invariant states by generalizing to
the non-commutative case Kakutani's work on wandering projections. This leads
on to a classification of the structure of the local algebra O(D) by using a
'T-Twisted' equivalence relation, including a full analysis of the T-type III
case. In particular we show that O(D) is T-type III if and only if the crossed
product algebra O(D)xT is type III in the sense of Murray-von Neumann.
