  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.
