Steady-state density large deviations in driven diffusive systems
Soumyabrata Saha, Tridib Sadhu · arXiv (Cornell University) · 2025
A diffusive system coupled to boundary reservoirs reaches a non-equilibrium steady state whose density fluctuations can exhibit correlations over macroscopic distances. While current fluctuations are well understood for generic systems, exact results for the steady-state density large-deviation functional remain restricted to a few special models. We introduce a field transformation within Macroscopic Fluctuation Theory that, in one dimension, captures two broad exactly solvable classes characterized respectively by local and non-local large-deviation functionals. The transformation also allows us to explicitly determine the optimal fluctuation paths, exposing the dynamical origin of non-locality and time irreversibility. For generic transport coefficients, the same transformation provides a systematic perturbative scheme in the boundary drive. In particular, we show that a finite bulk drive shifts the onset of non-locality from quadratic to linear order in the boundary drive and generically generates long-range connected multipoint correlations of arbitrarily high order. In higher dimensions, this onset depends on the orientation of the bulk drive relative to the boundary-induced density gradient.