We show that the fluctuations of the partial current in two dimensionaldiffusive systems are dominated by vortices leading to a different scaling fromthe one predicted by the hydrodynamic large deviation theory. This is supportedby exact computations of the variance of partial current fluctuations for thesymmetric simple exclusion process on general graphs. On a two-dimensionaltorus, our exact expressions are compared to the results of numericalsimulations. They confirm the logarithmic dependence on the system size of thefluctuations of the partialflux. The impact of the vortices on the validity ofthe fluctuation relation for partial currents is also discussed.
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