Ballistic macroscopic fluctuation theory via mapping to point particles

Ballistic Macroscopic Fluctuation Theory (BMFT) captures the evolution of fluctuations and correlations in systems where transport is strictly ballistic. We show that, for generic integrable particle models, BMFT can be constructed through a direct mapping onto ensembles of classical or quantum point particles. This mapping generalises the well-known correspondence between hard spheres and point particles: the two-body scattering shift now plays the role of an effective rod length for arbitrary interactions. Within this framework we re-derive both the full-counting statistics and the long-range correlation functions previously obtained by other means, thereby providing a unified derivation. Our results corroborate the general picture that all late-time fluctuations and correlations stem from the initial noise, subsequently convected by Euler-scale hydrodynamics.