Nonequilibrium shear viscosity computations with Langevin dynamics

TL;DR

This paper develops a mathematical framework using Langevin dynamics to estimate shear viscosity in nonequilibrium systems, relating stationary state averages to equilibrium expectations and analyzing velocity profiles.

Contribution

It introduces a linear response relation for nonequilibrium Langevin systems and derives methods to extract viscosity from velocity profiles under certain approximations.

Findings

Established a linear response formula linking nonequilibrium and equilibrium averages.

Derived a local conservation law for the fluid's velocity profile.

Analyzed asymptotic behavior of velocity profiles as friction parameters vary.

Abstract

We study the mathematical properties of a nonequilibrium Langevin dynamics which can be used to estimate the shear viscosity of a system. More precisely, we prove a linear response result which allows to relate averages over the nonequilibrium stationary state of the system to equilibrium canonical expectations. We then write a local conservation law for the average longitudinal velocity of the fluid, and show how, under some closure approximation, the viscosity can be extracted from this profile. We finally characterize the asymptotic behavior of the velocity profile, in the limit where either the transverse or the longitudinal friction go to infinity. Some numerical illustrations of the theoretical results are also presented.