  Macroscopic fluctuations have become an essential tool to understand physics
far from equilibrium due to the link between their statistics and
nonequilibrium ensembles. The optimal path leading to a fluctuation encodes key
information on this problem, shedding light on e.g. the physics behind the
enhanced probability of rare events out of equilibrium, the possibility of
dynamic phase transitions and new symmetries. This makes the understanding of
the properties of these optimal paths a central issue. Here we derive a
fundamental relation which strongly constraints the architecture of these
optimal paths for general $d$-dimensional nonequilibrium diffusive systems, and
implies a non-trivial structure for the dominant current vector fields.
Interestingly, this general relation (which encompasses and explains previous
results) makes manifest the spatio-temporal non-locality of the current
statistics and the associated optimal trajectories.
