Non-equilibrium projection-operator for a quenched thermostatted system

A projection operator formalism is presented which allows to derive an exact set of equations for correlation functions and susceptibilities in out of equilibrium situations of many particle systems. Explicitely considered is the case of an initial temperature quench in a simple liquid stabilized by a Gaussian thermostat. Implications for the violation of the fluctuation dissipation theorem in simple structural glass formers like Lennard-Jones glasses and colloidal glasses and the differences to the Kawasaki-Gunton projection operator are discussed.