Anomalous current fluctuations from Euler hydrodynamics

We consider the hydrodynamic origin of anomalous current fluctuations in a family of stochastic charged cellular automata. Using ballistic macroscopic fluctuation theory, we study both typical and large fluctuations of the charge current and reproduce microscopic results which are available for the deterministic single-file limit of the models. Our results indicate that in general initial fluctuations propagated by Euler equations fully characterize both scales of anomalous fluctuations. For stochastic dynamics, we find an additional contribution to typical fluctuations and conjecture the functional form of the typical probability distribution, which we confirm by numerical simulations.