  We introduce a new universal framework describing fluctuations and
correlations in quantum and classical many-body systems, at the Euler
hydrodynamic scale of space and time. The framework adapts the ideas of the
conventional macroscopic fluctuation theory (MFT) to systems that support
ballistic transport. The resulting "ballistic MFT" (BMFT) is solely based on
the Euler hydrodynamics data of the many-body system. Within this framework,
mesoscopic observables are classical random variables depending only on the
fluctuating conserved densities, and Euler-scale fluctuations are obtained by
deterministically transporting thermodynamic fluctuations via the Euler
hydrodynamics. Using the BMFT, we show that long-range correlations in space
generically develop over time from long-wavelength inhomogeneous initial states
in interacting models. This result, which we verify by numerical calculations,
challenges the long-held paradigm that at the Euler scale, fluid cells may be
considered uncorrelated. We also show that the Gallavotti-Cohen fluctuation
theorem for non-equilibrium ballistic transport follows purely from
time-reversal invariance of the Euler hydrodynamics. We check the validity of
the BMFT by applying it to integrable systems, and in particular the hard-rod
gas, with extensive simulations that confirm our analytical results.
