Critical-like slowdown in thermal soft-sphere glasses via energy minimization

Using hybrid molecular dynamics/SWAP Monte Carlo (MD/SMC) simulations, we show that while the terminal relaxation times τ(ϕ) for FIRE energy minimization of soft-sphere glasses can decrease by orders of magnitude as sample equilibration proceeds and the jamming density ϕ_{J} increases, they always scale as τ(ϕ)∼(ϕ_{J}-ϕ)^{-2}∼[Z_{iso}-Z_{ms}(τ)]^{-2}, where Z_{iso}=2d and Z_{ms}(τ) is the average coordination number of particles satisfying a minimal local mechanical stability criterion (Z≥d+1) at the top of the final potential-energy-landscape (PEL) sub-basin the system encounters. This scaling allows us to collapse τ datasets that look very different when plotted as a function of ϕ, and to address a closely related question: how does the character of the PEL basins that dense thermal glasses most typically occupy evolve as the glasses age at constant ϕ and T?