  We study a simple transport model driven out of equilibrium by reservoirs at
the boundaries, corresponding to the hydrodynamic limit of the symmetric simple
exclusion process. We show that a nonlocal transformation of densities and
currents maps the large deviations of the model into those of an open, isolated
chain satisfying detailed balance, where rare fluctuations are the time
reversals of relaxations. We argue that the existence of such a mapping is the
immediate reason why it is possible for this model to obtain an explicit
solution for the large-deviation function of densities through elementary
changes of variables. This approach can be generalized to the other models
previously treated with the macroscopic fluctuation theory.
