Mutual Linearity in Nonequilibrium Langevin Dynamics

TL;DR

This paper introduces a mutual linearity framework in nonequilibrium Langevin systems, enabling linear relations among stationary densities and currents, with applications to molecular motors.

Contribution

It establishes the mutual linearity property in nonequilibrium overdamped Langevin systems and extends it to non-stationary relaxation processes, providing a new control framework.

Findings

Stationary densities at different positions are linearly related under local perturbations.

Mutual linearity among stationary state-current observables is demonstrated.

The theory is robust under finite-width perturbations and applied to the F$_1$-ATPase rotary motor.

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$_1$-ATPase rotary motor model.