Large deviations and heterogeneities in a driven kinetically constrained model

Kinetically Constrained Models (KCMs) have been widely studied in the context of glassy dynamics, focusing on the influence of dynamical constraints on the slowing-down of the dynamics of a macroscopic system. In these models, it has been shown using the thermodynamic formalism for histories, that there is a coexistence between an active and an inactive phase. This coexistence can be described by a first-order transition, and a related discontinuity in the derivative of the large-deviation function for the activity. We show that adding a driving field to a KCM model does not destroy this first-order transition for the activity. Moreover, a singularity is also found in the large-deviation function of the current at large fields. We relate for the first time this property to microscopic structures, in particular the heterogeneous, intermittent dynamics of the particles, transient shear-banding and blocking walls. We describe both the shear-thinning and the shear-thickening regimes, and find that the behaviour of the current is well reproduced by a simple model