Hydrodynamic limit for the velocity flip model

TL;DR

This paper investigates the hydrodynamic limit of a chain of coupled oscillators with velocity flips, deriving macroscopic equations through entropy methods to understand energy diffusion.

Contribution

It introduces a novel approach to derive hydrodynamic equations for a velocity-flip oscillator chain using entropy estimates and local equilibrium modifications.

Findings

Hydrodynamic equations for the velocity flip model are derived.

The system exhibits diffusive energy transport under the velocity flip perturbation.

The method ensures good ergodic properties and local conservation of energy.

Abstract

We study the diffusive scaling limit for a chain of $N$ coupled oscillators. In order to provide the system with good ergodic properties, we perturb the Hamiltonian dynamics with random flips of velocities, so that the energy is locally conserved. We derive the hydrodynamic equations by estimating the relative entropy with respect to the local equilibrium state modified by a correction term.