Green-Kubo relations for nonequilibrium hydrodynamics transport coefficients

For near-equilibrium macroscopic transport, the fluctuation-dissipation theorem (FDT) has been used to link transport coefficients to correlation functions of local observables, a connection known as Green-Kubo relations. Although there are several known equalities that generalize the FDT around nonequilibrium steady states, none have led to the prediction of analogous nonequilibrium Green-Kubo relations. Here, we demonstrate that there is a class of perturbations whose response maintains the equilibrium-form of the FDT, yet remains valid arbitrarily far from equilibrium. As a consequence of this novel FDT, we derive Green-Kubo relations for nonequilibrium hydrodynamic transport coefficients without invoking Onsager's regression hypothesis. We illustrate the theoretical results with molecular dynamics simulations of interacting active Brownian particles. Our simulations show that the diffusion coefficient of active Brownian particles is determined by the fluctuations of the local particle density and its current.