Weak additivity principle for current statistics in d dimensions

The additivity principle (AP) allows one to compute the current distribution in many one-dimensional nonequilibrium systems. Here we extend this conjecture to general d-dimensional driven diffusive systems, and validate its predictions against both numerical simulations of rare events and microscopic exact calculations of three paradigmatic models of diffusive transport in d=2. Crucially, the existence of a structured current vector field at the fluctuating level, coupled to the local mobility, turns out to be essential to understand current statistics in d>1. We prove that, when compared to the straightforward extension of the AP to high d, the so-called weak AP always yields a better minimizer of the macroscopic fluctuation theory action for current statistics.