Thermodynamic metric of nonequilibrium steady states

Within the linear response regime, minimally dissipative~transitions~between~equilibrium states are given by the geodesics of a thermodynamic metric in~parameter~space. We~derive an analogous~geometric structure for transitions~between nonequilibrium steady~states, after a suitable renormalization of heat. With a novel expansion formula for the governing master equation, we propose an~exact~expression~for the metric.~As in~the equilibrium scenario, the components of the metric are given by the time-integrals of correlation functions in nonequilibrium steady states.