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.
Related
- Post-Newtonian secular dynamics of hierarchical triples. I. Eccentricity-, inclination- and node-dependence of the multiple-scale formulation, and its canonical consistency
- Improving Molecular Dynamics of Aqueous Electrolytes through Data-Driven Sensitivity-Guided GFN2-xTB Reparameterization
- Interaction dependence of the critical correlation length amplitude ratio in anisotropic scalar lattice ϕ4 theory
- High-Pressure Refractive Indices of NaCl, KCl, CaO, SrO, and MgO Reveal the Dependence of Anion Polarizability on Coordination Number and Bond Length
- UV/IR scale dependence in a four-derivative scalar field theory
BibTeX
@misc{ciamarra2026lengthscale,
title = {{Length-scale dependence of collective time reparameterization in swap dynamics}},
author = {Massimo Pica Ciamarra},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16168},
eprint = {2610.16168},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16168},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Length-scale dependence of collective time reparameterization in swap dynamics
AU - Massimo Pica Ciamarra
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16168
UR - https://arxiv.org/abs/2610.16168
AB - 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.
ER -