Length-scale dependence of collective time reparameterization in swap dynamics

Abstract

Swap Monte Carlo dramatically accelerates the equilibration of deeply supercooled liquids while preserving the equilibrium Boltzmann distribution. Recent work has argued that swap and other accelerated algorithms act by reparameterizing time: different dynamics follow the same slow relaxation process, but with different clocks. Here we test this idea in a continuously polydisperse glass former. We confirm that mean collective overlaps satisfy an approximate time reparameterization, in agreement with earlier results. However, the associated clock depends systematically on the collective probe length and on the relaxation stage. Thus the observed collective collapse does not define a unique, observable-independent material time. Over the numerically accessible $α$-relaxation regime, swap changes not only the rate of relaxation, but also its length-scale dependence. The resulting collective reparameterization is therefore only approximate and does not establish an exact dynamical equivalence between swap and reference relaxation.