# Nonequilibrium Langevin dynamics: a demonstration study of shear flow fluctuations in a simple fluid

## TL;DR

This paper demonstrates how second-order Langevin dynamics can accurately model shear flow fluctuations in a simple fluid, combining theoretical derivation with numerical simulation to validate the approach.

## Contribution

It determines all stochastic parameters for a second-order Langevin model of shear flow and compares the model directly with molecular dynamics data.

## Key findings

- The Langevin model accurately reproduces flow autocorrelations.
- A linear relation between external force and flow fluctuation cumulants is identified.
- Introduction of a new quantity: athermal cumulant ratio.

## Abstract

The present study is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the related deterministic parameters of the Langevin equation for a Couette flow in a microscopic Molecular Dynamics model of a simple fluid. In this paper we find all the remaining constants of the stochastic dynamics, which is then numerically simulated and directly compared with the original physical system. By using these data, we study in detail the accuracy and precision of a second-order Langevin model for nonequilibrium physical systems, theoretically and computationally. In addition, an intriguing relation is found between an applied external force and cumulants of the resulting flow fluctuations. This is characterized by a linear dependence of athermal cumulant ratio, a new quantity introduced here.