  We study the universal thermodynamic properties of systems consisting of many
coupled oscillators operating in the vicinity of a homogeneous oscillating
instability. In the thermodynamic limit, the Hopf bifurcation is a dynamic
critical point far from equilibrium described by a statistical field theory. We
perform a perturbative renormalization group study, and show that at the
critical point a generic relation between correlation and response functions
appears. At the same time the fluctuation-dissipation relation is strongly
violated.
