Derivation of Hydrodynamics from the Hamiltonian description of particle systems

TL;DR

This paper derives an exact hydrodynamic equation from Hamiltonian particle systems, connecting microscopic dynamics to macroscopic fluid behavior using statistical and perturbative methods.

Contribution

It introduces an exact derivation of hydrodynamics from Hamiltonian systems assuming local Gibbs distribution, employing fluctuation theorem-like identities.

Findings

Derivation of an exact evolution equation for density fields

Recovery of Navier-Stokes equations via perturbation expansion

Establishment of a link between microscopic Hamiltonian dynamics and macroscopic fluid equations

Abstract

Hamiltonian particle systems may exhibit non-linear hydrodynamic phenomena as the time evolution of the density fields of energy, momentum, and mass. In this Letter, an exact equation describing the time evolution is derived assuming the local Gibbs distribution at initial time. The key concept in the derivation is an identity similar to the fluctuation theorems. The Navier-Stokes equation is obtained as a result of simple perturbation expansions in a small parameter that represents the scale separation.