  We employ the macroscopic fluctuation theory to study fluctuations of
integrated current in one-dimensional lattice gases with a step-like initial
density profile. We analytically determine the variance of the current
fluctuations for a class of diffusive processes with a density-independent
diffusion coefficient, but otherwise arbitrary. Our calculations rely on a
perturbation theory around the noiseless hydrodynamic solution. We consider
both quenched and annealed types of averaging (the initial condition is allowed
to fluctuate in the latter situation). The general results for the variance are
specialized to a few interesting models including the symmetric exclusion
process and the Kipnis-Marchioro-Presutti model. We also probe large deviations
of the current for the symmetric exclusion process. This is done by numerically
solving the governing equations of the macroscopic fluctuation theory using an
efficient iteration algorithm.
