Dynamical Phase Transitions in boundary driven systems: Classification, examples and (some) intuition

Phase transitions are of unfading interest. While classical systems in equilibrium present no phase transitions in 1 dimension, they can be manifested in systems driven out of equilibrium. In this talk we will explore the current fluctuations in boundary driven systems. Current fluctuations are explored by the probability to observe an atypical current over a long period of time. We will show a few examples of phase transitions and classify them. For a special kind of phase transitions, we will show a mapping to a single particle evolving under classical Lagrangian mechanics. This mapping  provides us with a simple picture of where one could expect such transitions.