Affine relationships between steady currents
Abstract
Perturbing transition rates in a steady nonequilibrium system, e.g. modelled 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 currents. Such a nonperturbative interrelation was discovered by P.E. Harunari et al. in [1] by applying algebraic graph theory showing the mutual linearity of currents over different edges in a graph. 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.
Cite
@article{arxiv.2412.05019,
title = {Affine relationships between steady currents},
author = {Faezeh Khodabandehlou and Christian Maes and Karel Netočný},
journal= {arXiv preprint arXiv:2412.05019},
year = {2025}
}