Hydrodynamics without Averaging -- a Hard Rods Study

TL;DR

This paper investigates the validity of generalized hydrodynamics in the integrable hard rods model without averaging over local equilibrium, revealing the absence of intrinsic diffusion and applicability to non-thermal states.

Contribution

It introduces a novel approach to hydrodynamics that avoids local equilibrium assumptions, clarifying diffusion mechanisms in integrable models.

Findings

Intrinsic diffusion is absent in the hard rods model.

Hydrodynamics applies to non-thermal states.

Disentangles diffusion from convection effects.

Abstract

On the example of the integrable hard rods model we study the quality of the (generalized) hydrodynamic approximation on a single coarse-grained sample. This is opposed to the traditional approach which averages over an appropriate local equilibrium state. While mathematically more ambiguous, a major advantage of the new approach is that it allows us to disentangle intrinsic diffusion from `diffusion from convection' effects. For the hard rods we find intrinsic diffusion is absent, which agrees with and clarifies recent findings. Interestingly, the results also apply to not locally thermal states, demonstrating that hydrodynamics (in this model) does not require the assumption of local equilibrium.