  Many natural, technological and social systems are inherently not in
equilibrium. We show, by detailed analysis of exemplar models, the emergence of
equilibrium-like behavior in localized or nonlocalized domains within
non-equilibrium systems as conjectured in some real systems. Equilibrium
domains are shown to emerge either abruptly or gradually depending on the
system parameters and disappear, becoming indistinguishable from the remainder
of the system for other parameter values. The models studied, defined on
densely and sparsely connected networks, provide a useful representation of
many real systems.
