Non-equilibrium pathways between cluster morphologies in active phase separation: necking, rupture and cavitation

TL;DR

The paper investigates non-equilibrium pathways between slab and droplet morphologies in a 2D active lattice gas exhibiting motility-induced phase separation. Using forward flux sampling, it characterizes reactive trajectories for both slab-to-droplet and droplet-to-slab transitions across four state points spanning different Peclet numbers, with two order parameters $d$ and $s$ guiding the transition analysis. It finds that droplet-to-slab transitions are largely equilibrium-like, while slab-to-droplet transitions exhibit non-equilibrium mechanisms, including indentation with interior bubbles at low $Pe$ and large bubble–mediated rupture at high $Pe$, driven by persistent fluctuations rather than time-reversed pathways. These results highlight how non-equilibrium fluctuations, such as vapour bubbles, can fundamentally alter transition mechanisms in active matter, and suggest the need for enhanced order parameters and theoretical descriptions to capture such effects.

Abstract

We investigate the dynamical pathways of a geometric phase transition in a two-dimensional active lattice gas undergoing motility-induced phase separation. The transition is between metastable morphologies of the liquid cluster: a system-spanning "slab" and a compact "droplet". We generate trajectories of this transition in both directions using forward flux sampling. We find that the droplet-to-slab transition always follows a similar mechanism to its equilibrium counterpart, but the reverse (slab-to-droplet) transition depends on rare non-equilibrium fluctuations. At low Peclet numbers the equilibrium and non-equilibrium pathways compete, while at high Peclet numbers the equilibrium pathway is entirely suppressed, and the only allowed mechanism involves a large vapour bubble. We discuss the implications of these findings for active matter systems more generally.

Figures (7)

• Figure 1: Illustration showing the definition of the reaction coordinate $d$, when the system is in the slab (left) or droplet (right) geometry.
• Figure 2: (a,b) Average transition trajectories of parameters A1 (left column) and A2 (right column). (c,d) 100 sample trajectories of the droplet to slab transition for each parameter set. (e,f) 100 sample trajectories of the slab to droplet transition. The shadings indicate the probability distributions within the metastable basins, obtained by direct sampling. All trajectories are obtained using FFS runs with $N_c = 16000$.
• Figure 3: Time-ordered snapshots taken from simulations of parameters A1, showing trajectories of (a) the formation of a slab from a droplet, (b,c) Two trajectories showing the slab-to-droplet transition showing an equilibrium-like mechanism (column b) and a non-equilibrium one (column c).
• Figure 4: (a) Averaged reactive trajectories for parameters A2 with various values of $N_c$. The shaded densities indicate probability distributions within of the metastable basins. (b), (c) The effective sample size at the initial milestone $N_{\mathrm{eff}}$ plotted against $N_c$.
• Figure 5: Top to bottom: average transition trajectories of parameters (a) B1 and (b) B2; 100 sample trajectories of the droplet to slab transition for (c) B1 and (d) B2; 100 sample trajectories of the slab to droplet transition for (e) B1 and (f) B2. The density plots indicate the locations of the metastable basins. All trajectories are obtained using FFS runs with $N_c = 2000$.