  We examine the nonequilibrium nature of two-phase fluid displacements in a
quasi-two-dimensional medium (a model open fracture), in the presence of
localized constrictions ("defects"), from a theoretical and numerical
standpoint. Our analysis predicts the capillary energy dissipated in abrupt
interfacial displacements (jumps) across defects, and relates it to the
corresponding hysteresis cycle, e.g. in pressure-saturation. We distinguish
between "weak" (reversible interface displacement, exhibiting no hysteresis and
dissipation) and "strong" (irreversible) defects. We expose the emergence of
dissipation and irreversibility caused by spatial interactions, mediated by
interfacial tension, among otherwise weak defects. We exemplify this
cooperative behavior for a pair of weak defects and establish a critical
separation distance, analytically and numerically, verified by a
proof-of-concept experiment.
