In condensed matter science the glass transition is the paradigm for the slowdown and dynamical arrest into non-equilibrium states which is found to occur in a vast range of many-body systems.
While the theoretical understanding of this phenomenon is still under debate, an important lesson is that dynamical behaviour can be far richer and more complex than what static properties often suggest. A proper characterisation of dynamics therefore requires a method which focusses on statistical properties of trajectories. Via large deviation techniques such a “thermodynamics of trajectories” method can be readily devised.
In this talk I will review the glass transition problem, describe basic ideas for modelling slow dynamics, and explain what the dynamical large deviation approach tells us about glasses and non-equilibrium more generally.