Active Liquid-Liquid Phase-Separation in a Confining Environment

Active liquid-liquid phase separation (LLPS) in a confining environment is believed to play an important role in cell biology. Recently, it was shown that when active noise at the microscopic level is included in the classical theory of nucleation and growth then this does not cause the breakdown of detailed balance at the $\mathit{\text{macroscopic}}$ level provided that the droplet radius is the only collective coordinate. Here, we present a simple model for active LLPS in a confining environment, with the droplet location in a confining potential as a second collective coordinate, and find that detailed balance $\mathit{\text{is}}$ broken at the macroscopic level in an unusual fashion, using the Fluctuation-Dissipation Theorem as a diagnostic.