Thermal onset of the critical slowing down of soft-sphere glasses' energy-minimization dynamics

Several recent studies have shown that characteristic relaxation time τ^* for energy minimization in athermal soft-sphere glasses diverges as τ^* ~ (φ_J - φ)^-2, where φ_J is the jamming density. These studies all examined systems where φ_J ~= φ_RCP, raising the question of whether/how these diverging relaxation times depend on sample preparation protocol. Here we show that in thermal soft-sphere glasses equilibrated using SWAP Monte Carlo, the times required for systems to enter their final potential-energy-landscape (PEL) sub-basin during FIRE energy minimization (τ_FIRE) exhibit thermal onset as samples become increasingly well-equilibrated. We show that although τ_FIRE(φ) can decrease by orders of magnitude as sample equilibration proceeds and φ_J increases via thermal onset, it always scales as τ_FIRE ∼ (φ_J − φ)⁻² ∼ [Z_iso − Z_nr(τ_FIRE)]⁻², where Z_nr is the average coordination number of non-rattlers at the top of the final sub-basin. This common scaling allows us to (nearly) collapse τ_FIRE datasets that look very different when plotted as a function of φ, and to partially answer another closely related fundamental question: how does the character of the PEL basins thermal soft-sphere glasses most typically occupy evolve as they age at constant φ?