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 large and typical fluctuations of the charge current and reproduce microscopic results available for the deterministic single-file limit of the models. Our results indicate that, in general, initial fluctuations propagated by Euler equations fully characterize anomalous fluctuations on both scales. In the stochastic case, we find an additional contribution to typical fluctuations and conjecture the functional form of the typical probability distribution, which agrees with numerical simulations.