Lectures on non-equilibrium active systems

These notes are based on lectures given during the Summer School `Active matter and non-equilibrium statistical physics', held in Les Houches in September 2018. In these notes, we have merged our lectures into a single chapter broadly dedicated to `Non-equilibrium active systems'. We start with a discussion of generic features of non-equilibrium statistical mechanics, followed by a description of selected examples of the possible consequences of not being at thermal equilibrium. We then introduce the topic of dense glassy materials with a short review of glassy dynamics, rheology and jamming transitions for systems that are not active. We then discuss dense active materials, from simple mean-field theories to numerical models and experimental realizations. Finally, we discuss two examples of materials driven out of equilibrium by an oscillatory driving force.