Classical Nucleation Theory for Active Fluid Phase Separation

TL;DR

This paper extends classical nucleation theory to active fluids, analytically computing nucleation barriers in non-equilibrium systems by revealing a restored detailed balance along the critical nucleation pathway.

Contribution

It introduces an analytical approach to compute nucleation barriers in active phase separating systems using a minimal field-theoretic model, bridging passive and active nucleation theories.

Findings

Analytical expression for the quasi-potential in active phase separation.

Restoration of detailed balance along the nucleation pathway.

Nucleation barrier dependence on activity and supersaturation.

Abstract

Classical nucleation theory (CNT), linking rare nucleation events to the free energy landscape of a growing nucleus, is central to understanding phase-change kinetics in passive fluids. Nucleation in non-equilibrium systems is much harder to describe because there is no free energy, but instead a dynamics-dependent quasi-potential that typically must be found numerically. Here we extend CNT to a class of active phase separating systems governed by a minimal field-theoretic model (Active Model B+). In the small noise and supersaturation limits that CNT assumes, we compute analytically the quasi-potential, and hence nucleation barrier, for liquid-vapor phase separation. Crucially to our results, detailed balance, although broken microscopically by activity, is restored along the instanton trajectory, which in CNT involves the nuclear radius as the sole reaction coordinate.