Analysis of slow transitions between nonequilibrium steady states

Transitions between nonequilibrium steady states obey a generalized Clausius inequality, which becomes an equality in the quasistatic limit. For slow but finite transitions, we show that the behavior of the system is described by a response matrix whose elements are given by a far-from-equilibrium Green-Kubo formula, involving the decay of correlations evaluated in the nonequilibrium steady state. This result leads to a fluctuation-dissipation relation between the mean and variance of the nonadiabatic entropy production, $\Delta s_{\rm na}$. Furthermore, our results extend -- to nonequilibrium steady states -- the thermodynamic metric structure introduced by Sivak and Crooks for analyzing minimal-dissipation protocols for transitions between equilibrium states.