Abstract

First-order nonequilibrium phase transitions observed in active matter, fluid dynamics, biology, climate science, and other systems with irreversible dynamics are challenging to analyze because they cannot be inferred from a simple free energy minimization principle. Rather, the mechanism of these transitions depends crucially on the system’s dynamics, which requires us to analyze them in trajectory space rather than in phase space. Here we consider situations where the path of the transitions between competing metastable states can be characterized as the minimizer of an action, whose minimum value can be used in a nonequilibrium generalization of the Arrhenius law. We also introduce a new numerical tool for the minimization of this action. This tool is general enough to be transportable to many situations of interest, in particular when the fluctuations in the microscopic system are non-Gaussian and the dynamics is not governed by the standard Langevin equation with additive noise. As an illustration of the method, I will pinpoint the first-order phase transition of two spatially-extended nonequilibrium systems: the one of a reaction-diffusion network based on the Schlögl model, and the one of the Active Model B, the natural nonequilibrium extension of the Cahn-Hilliard dynamics. Notably, the paths of the transitions, including their critical nuclei, are identified.

Ref: Minimum Action Method for Nonequilibrium Phase Transitions, Ruben Zakine and Eric Vanden-Eijnden, https://arxiv.org/abs/2202.06936