Islands of equilibrium in a dynamical world

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.