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We show how to apply the macroscopic fluctuation theory (MFT) of Bertini, DeSole, Gabrielli, Jona-Lasinio, and Landim to study the current fluctuations ofdiffusive systems with a step initial condition. We argue that one has todistinguish between two ways of averaging (the annealed and the quenched cases)depending on whether we let the initial condition fluctuate or not. Althoughthe initial condition is not a steady state, the distribution of the currentsatisfies a symmetry very reminiscent of the fluctuation theorem. We show howthe equations of the MFT can be solved in the case of non-interactingparticles. The symmetry of these equations can be used to deduce thedistribution of the current for several other models, from its knowledge forthe symmetric simple exclusion process. In the range where the integratedcurrent $Q_t \sim \sqrt{t}$, we show that the non-Gaussian decay $\exp [-Q_t^3/t]$ of the distribution of $Q_t$ is generic.

Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile