Deep supercooling of Hard-Sphere fluids using metadynamics sampling

Hard-sphere fluids (and their soft-sphere cousins) have proven very fruitful models for understanding the glass and jamming transitions. Previous studies have identified polydisperse sphere fluids that completely avoid crystallization, and using state of the art methods such as swap Monte Carlo, equilibrated them up to unprecedented high volume fractions well above the glass transition. Outstanding questions include the existence of a Kauzmann density above which the entropy of the equilibrium fluid becomes sub-extensive, and the nature of jammed states above that density.  Here we use a metadynamics-inspired sampling method to efficiently equilibrate HS fluids at very high volume fractions.  Unlike conventional `basin-filling' metadynamics that operates on a reduced dimensional space, we operate in the full 3N-dimensional configuration space of the fluid.  Remarkably, we find that within a small window of bias potential properties, HS fluid configurations rapidly equilibrate under biased relaxation. The rate of such relaxation is only weakly sensitive to volume fraction.  The observed fluid states have a pressure that is well described by the Carnahan-Starling equation of state up to the highest volume fraction we studied, Φ = 0.670.  Curiously, such deeply supercooled HS fluids are difficult to compress using conventional jamming approaches.