  Near equilibrium, where all currents of a system vanish on average, the
fluctuation-dissipation relation (FDR) connects a current's spontaneous
fluctuations with its response to perturbations of the conjugate thermodynamic
force. Out of equilibrium, fluctuation-response relations generally involve
additional nondissipative contributions. Here, in the framework of stochastic
thermodynamics, we show that an equilibrium-like FDR holds for internally
equilibrated currents, if the perturbing conjugate force only affects the
microscopic transitions that contribute to the current. We discuss the physical
requirements for the validity of our result and apply it to nano-sized
electronic devices.
