Predicting phase transitions in nonequilibrium systems

Predicting phase transitions in thermal systems is one of the major achievements of equilibrium statistical mechanics. The situation is more difficult for nonequilibrium systems, in which energy or momentum is continuously injected, and there is a lack of a unifying theory that would give the phase transitions in that context. Here, we will show how a deterministic numerical method based on large deviation theory allows us to infer the nontrivial phase diagrams of nonequilibrium systems that display metastability. Our method proves useful to analyze bistability in reaction-diffusion systems, or to predict the collective behavior of active particles, for which a meanfield description pinpoints the accessible phases of the system. In particular, we are able to find the critical nucleus that drives the system from one metastable phase to another. Controlled experiments, involving swimming droplets which undergo short-range interactions while experiencing tunable birth-death dynamics (injection and dissolution), therefore represent a playground in which to test our approach.