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, is typically understood on thermodynamic grounds through the prism of classical nucleation theory. In this Letter, we revisit homogeneous nucleation from a purely mechanical perspective, elucidating the mechanical criteria for the size and density of a critical nucelus. Applying this theory to active fluids, we demonstrate 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. Crucially, however, we find that three distinct surface tensions - the mechanical, capillary, and Ostwald tensions - all play a role in the nucleation of active fluids. While these three surface tensions are identical in equilibrium, our work makes clear that there is no single surface tension that characterizes active fluid interfaces.