(319e) The Mechanics of Classical Nucleation and the Surface Tensions of Active Matter

The theoretical description of the transition path between two stable stationary states is an arduous challenge for all but the simplest systems. Homogeneous nucleation, a textbook example of a transition between stationary states of uniform density and phase separation, is typically understood on thermodynamic grounds through the prism of classical nucleation theory. In this talk, we revisit homogeneous nucleation from a purely mechanical perspective, elucidating the criteria for the size and density of a critical nucleus. Applying this theory to active fluids, we find that the nucleation of motility-induced phases proceeds in a qualitatively similar fashion to equilibrium systems, with concepts such as the Gibbs-Thomson effect and nucleation barriers remaining valid. We further demonstrate that the recovery of such concepts allows for existing for classical theories of nucleation rates and coarsening dynamics to be extended to active systems, provided one uses the appropriate definitions of the nucleation barrier and surface tensions. Three distinct surface tensions -- the mechanical, capillary, and Ostwald tensions -- play central roles in our theory. While these three surface tensions are identical in equilibrium, our work highlights the distinctive role of each of tension in the stability of active interfaces and the nucleation and growth of motility-induced phases.