Energy fluctuations, hydrodynamics and local correlations in harmonic systems with bulk noises

TL;DR

This paper compares two harmonic systems with bulk noises that have similar steady states but different hydrodynamic behaviors, providing insights into nonequilibrium dynamics and effective modeling.

Contribution

It highlights how systems with similar steady states can exhibit different convergence behaviors, informing the development of predictive models for nonequilibrium systems.

Findings

Two systems share the same thermal conductivity and two-point functions.

Their convergence towards steady states differs significantly.

Results inform effective modeling of nonequilibrium dynamical systems.

Abstract

In this note, I summarise and comment on joint work with C. Bernardin, V. Kannan and J. L. Lebowitz concerning two harmonic systems with bulk noises whose nonequilibrium steady states (NESS) are nearly identical (they share the same thermal conductivity and two-point function), but whose hydrodynamic properties (convergence towards the NESS) are very different. The goal is to discuss the results in the general context of nonequilibrium properties of dynamical systems, in particular, what they tell us about possible effective models, or predictive approximations, for such systems.