Fluctuation dissipation relations far from equilibrium

In this paper we review some recent progress in the field of non-equilibrium linear response theory. We show how a generalization of the. fluctuation dissipation theorem can be derived for Markov processes, and discuss the Cugliandolo-Kurchan fluctuation dissipation relation for ageing systems and the theorem by Franz et al relating static and dynamic properties. We than specialize to phase ordering systems, examining the scaling properties of the linear response function and how these are determined by the behaviour of topological defects. We discuss how the connection between statics and dynamics can be violated in these systems at the lower critical dimension or due to stochastic instability.