Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas.

A recently developed nonlinear fluctuating hydrodynamics theory has been quite successful in describing various features of anomalous energy transport. However, the diffusion and the noise terms present in this theory are not derived from microscopic descriptions but rather added phenomenologically. We here derive these hydrodynamic equations with explicit calculation of the diffusion and noise terms in a one-dimensional model.