Dynamics of dilute gases at equilibrium: from the atomistic description to fluctuating hydrodynamics

TL;DR

This paper derives linear fluctuating hydrodynamics from a deterministic particle system at equilibrium in the low-density limit, connecting atomistic descriptions to macroscopic fluctuation theories.

Contribution

It provides a rigorous derivation of fluctuating hydrodynamics from first principles for dilute gases at equilibrium, extending previous covariance and Wick rule results.

Findings

Established the low-density limit of particle systems leads to fluctuating hydrodynamics.

Connected atomistic models with macroscopic fluctuation descriptions.

Built upon previous covariance asymptotics and Wick rule proofs.

Abstract

We derive linear fluctuating hydrodynamics as the low density limit of a deterministic system of particles at equilibrium. The proof builds upon previous results of the authors where the asymptotics of the covariance of the fluctuation field is obtained, and on the proof of the Wick rule for the fluctuation field.