Species interconversion of deformable particles yields transient phase separation

We consider a dense assembly of repulsive particles whose fluctuating sizes are subject to an energetic landscape that defines three species: two distinct states of particles with a finite size, and point particles as an intermediate state between the two previous species. We show that the non-equilibrium synchronization of sizes systematically leads to a homogeneous configuration associated with the survival of a single species. Remarkably, the relaxation towards such a configuration features a transient phase separation. By delineating and analyzing the dominant kinetic factors at play during relaxation, we recapitulate the phase diagram of species survival in terms of the parameters of the size landscape. Finally, we obtain a hydrodynamic mapping to equilibrium by coarse-graining the microscopic dynamics, which leads to predicting the nature of the transitions between various regimes where distinct species survive.