Mutual Linearity in Nonequilibrium Langevin Dynamics
Abstract
Understanding how nonequilibrium systems respond to perturbations is a central challenge in physics. In this work, we establish mutual linearity in nonequilibrium overdamped Langevin systems. This theory provides a framework for controlling and designing nonequilibrium responses in continuous systems. When a dynamical parameter is locally perturbed at a single position, the stationary densities at any two positions are linearly related. It further leads to mutual linearity among different stationary state-current observables. We also extend the mutual linearity to non-stationary relaxation processes in the Laplace domain. Our theory reveals that mutual linearity in both discrete and continuous systems originates from the same one-dimensional response structure. We further show that mutual linearity is robust under finite-width perturbations. As an application, we demonstrate the mutual linearity and its finite-width robustness in the F-ATPase rotary motor model.
Cite
@article{arxiv.2605.07949,
title = {Mutual Linearity in Nonequilibrium Langevin Dynamics},
author = {Jiming Zheng and Zhiyue Lu},
journal= {arXiv preprint arXiv:2605.07949},
year = {2026}
}