  We report opposite statistical mechanical behaviors of the two major
paradigms in which quantum correlation measures are defined, viz., the
entanglement-separability paradigm and the information-theoretic one. We show
this by considering the ergodic properties of such quantum correlation measures
in transverse quantum XY spin-1/2 systems in low dimensions. While entanglement
measures are ergodic in such models, the quantum correlation measures defined
from an information-theoretic perspective can be nonergodic.
