"Large non-equilibrium fluctuations in diffusive lattice gases":
In thermal equilibrium, fluctuations of macroscopic quantities are fully described in terms of the free energy of the system. Non-equilibrium fluctuations are much harder to describe, especially when they are large. An important recent advance is the elucidation of the behavior of fluctuations, including large deviations, of macroscopic observables in non-equilibrium steady states of driven diffusive lattice gases: simple classical transport systems with particle conservation. Here we deal with non-stationary settings and ask the following question: What is the probability that an unusual event occurs in a diffusive lattice gas during a specified time T? One such an unusual event is formation of a macroscopic void in an initially homogeneous gas. Another example deals with extreme statistics of current passing through a specified point during a specified time. We address these questions by employing the Macroscopic Fluctuation Theory (MFT), developed in the last decade by Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim. The MFT not only yields the desired probability, but also predicts the most likely gas density history leading to the specified rare event.