Affine relationships between steady currents

Abstract Perturbing transition rates in a steady nonequilibrium system, e.g. modeled by a Markov jump process, causes a change in the local currents. Their susceptibility is usually expressed via Green–Kubo relations or their nonequilibrium extensions. However, we may also wish to directly express the mutual relation between steady currents over different edges of the same network. Such a nonperturbative interrelation was discovered by Harunari et al (2024 Phys. Rev. Lett. 133 047401) by applying algebraic graph theory showing the mutual linearity of steady currents. We give a novel and shorter derivation of that current relationship where we express the current–current susceptibility as a difference in mean first-passage times. It allows an extension to multiple currents, which remains affine but the relation is not additive.