Active liquid-liquid phase separation in a confining environment

Liquid-liquid phase separation (LLPS) in a confining environment is believed to play an important role in cell biology. At least in some cases, this form of LLPS involves free energy consumption, which could lead to breakdown of the fundamental Principle of Detailed Balance (PDB). Recently, it was shown that when active noise at the microscopic level is included in the classical theory of nucleation and growth this does not cause the breakdown of detailed balance at the 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 functioning as a second collective coordinate. Using the Fluctuation-Dissipation Theorem as a diagnostic, we show that the PDB now is broken at the macroscopic level but in an unusual fashion: the active noise suppresses both the linear susceptibility and the quasicritical thermal noise spectrum in an asymmetric manner.