Quasi-static properties of Markovian systems in metastable state: Fluctuation-dissipation theorem

We show detailed calculations to obtain a metastable fluctuation-dissipation theorem (FDT) for Markovian systems with detailed balance. This is done by taking, for the metastable probability distribution, a superposition of the ground and the first excited state of the corresponding master operator. We apply perturbation theory to the master equation using, as initial condition, the metastable distribution. The metastable susceptibility is obtained using linear response. It is shown that this metastable susceptibility can be written in terms of the transform of the appropriately defined metastable correlations. The metastable (FDT) is valid for times shorter than the nucleation time of the metastable state.