Activity statistics of a forced elastic string in a disordered medium

We use a discrete model to study the non-equilibrium dynamics of a slowly driven elastic string in a two-dimensional disordered medium at finite temperatures. We focus on the local activity statistics to show that it can be related to global observables like the average interface velocity and the temporal correlations of the velocity fluctuations. For low temperatures the string exhibits typical creep motion and the activity statistics follows a power law, consistent with an exponential distribution of energy barriers. However, we find that the activity statistics is essentially different when the temperature is low enough, suggesting a different relaxation mechanism as T -> 0. We argue that this is due to the generic non-equilibrium nature of our model in the absence of thermal fluctuations.