  We propose a measure for genuine multipartite correlations suited for the
study of dynamics in open quantum systems. This measure is contextual in the
sense that it depends on how information is read from the environment. It is
used to study an interacting collective system of atoms undergoing phase
transitions as external parameters are varied. We show that the steady state of
the system can have a significant degree of genuine multipartite quantum and
classical correlations, and that the proposed measure can serve as a witness of
critical behavior in quantum systems.
