Simulating generalized fluids via interacting wave packet evolution

One–dimensional integrable and integrable systems display, on macroscopic scales, a universal form of transport known as (GHD). In its standard Euler-scale formulation, GHD mirrors the equations of a two-dimensional compressible fluid but ignores fluctuations and becomes numerically unwieldy as soon as integrability-breaking perturbations are introduced. We show that GHD can be efficiently simulated as a gas of —a natural generalization of hard-rod particles—whose trajectories are efficiently mapped onto those of point particles. This representation (i) provides a transparent route to incorporate integrability-breaking terms, and (ii) automatically embeds the exact fluctuating-hydrodynamics extension of GHD. The resulting framework enables fast, large-scale simulations of quasi-integrable systems even in the presence of complicated integrability-breaking perturbations. It also manifests the pivotal role of two-point correlations in systems confined by external potentials: we demonstrate that situations where local one-point observables appear thermalized can nevertheless sustain long-lived, far-from-equilibrium correlations for arbitrarily long times, signaling that, differently from what was previously stated, true thermalization is reached at diffusive time-scales.