Elucidating rates of rare transitions in nonequilibrium systems via optimal pathways

Unlike their equilibrium counterparts, rare nonequilibrium transitions are not governed by the energetics of static transition states. This renders efficient equilibrium techniques for computing rates and elucidating mechanisms largely invalid. Instead, reaction rates in systems driven far from thermodynamic equilibrium are dependent on the details of their trajectories. In the weak-noise limit, these transitions are dominated by the optimal transition path or instanton.

In our recent work, we developed a numerically efficient and broadly applicable instanton method to calculate the rate constant of rare transitions between nonequilibrium steady states of driven systems. In addition to intuitive insight into the transition mechanism, this nonequilibrium instanton rate theory provides accurate quantitative predictions of the transition rate in both active particle and field theories, including systems featuring underdamped dynamics and state-dependent noise. In this presentation, we will build on previous work and demonstrate how instanton rate theories can be applied to quantify and understand rare nonequilibrium transitions across a diverse range of systems, from phase transitions in active field theories to reactions of particles driven by a time-dependent external field.