Baruch Meerson, Pavel V. Sasorov
We use the macroscopic fluctuation theory (MFT) to study large current fluctuations in non-stationary diffusive lattice gases. We identify two universality classes of of these fluctuations which we call elliptic and hyperbolic. They emerge in the limit when the deterministic mass flux is small compared to the mass flux due to the shot noise. The two classes are determined by the sign of compressibility of an effective fluid, obtained by mapping the MFT into inviscid hydrodynamics. An example of the elliptic class is the Symmetric Simple Exclusion Process where, for some initial conditions, we can solve the effective hydrodynamics exactly. This yields the optimal path of the system and leads to a super-Gaussian statistics of large currents conjectured by Derrida and Gerschenfeld (2009). For models belonging to the hyperbolic class the deterministic mass flux cannot be neglected, leading to a different large-current statistics.
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http://arxiv.org/abs/1307.1867
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