Symmetry-breaking in the dynamical fluctuations of driven diffusive systems

Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. In this talk I will shed light on both the macroscopic large deviation properties and the microscopic origin of such spontaneous symmetry breaking in the paradigmatic weakly asymmetric exclusion process. By studying the joint fluctuations  of the current and a collective order parameter, I will uncover the full dynamical phase diagram for arbitrary boundary driving. The associated joint large deviation function becomes non-convex below the critical point, where a Maxwell-like violation of the additivity principle is observed. At the microscopic level, the dynamical phase transition is linked to an emerging degeneracy of the ground state of the microscopic generator, from which the optimal trajectories in the symmetry-broken phase follow. Finally, I will show how this new symmetry-breaking phenomenon is observed in extensive rare-event simulations of the microscopic dynamics.