Using the fluctuation-dissipation theorem for nonconservative forces

TL;DR

This paper shows that under certain conditions, the fluctuation-dissipation theorem can be extended to some nonconservative forces in nonequilibrium steady states, especially using symmetry considerations for linear force fields.

Contribution

It introduces a method to apply the fluctuation-dissipation theorem to specific nonconservative forces by exploiting a symmetry-based freedom in linear response theory.

Findings

The fluctuation-dissipation theorem can be valid for certain nonconservative forces.

A response formula for shear forces is derived, offering improved statistical accuracy.

Symmetry considerations enable the extension of fluctuation-dissipation relations to nonconservative systems.

Abstract

An equilibrium system which is perturbed by an external potential relaxes to a new equilibrium state, a process obeying the fluctuation-dissipation theorem. In contrast, perturbing by nonconservative forces yields a nonequilibrium steady state, and the fluctuation-dissipation theorem can in general not be applied. Here we exploit a freedom inherent to linear response theory: Force fields which perform work that does not couple statistically to the considered observable can be added without changing the response. Using this freedom, we demonstrate that the fluctuation-dissipation theorem can be applied for certain nonconservative forces. We discuss the case of a nonconservative force field linear in particle coordinates, where the mentioned freedom can be formulated in terms of symmetries. In particular, for the case of shear, this yields a response formula, which we find advantageous over the known Green-Kubo relation in terms of statistical accuracy.