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Clever algorithms for glasses work by time reparameterization.

Federico Ghimenti1,2, Ludovic Berthier3,4, Jorge Kurchan5

  • 1Laboratoire Matière et Systèmes Complexes, Université Paris Cité & CNRS (UMR 7057), Paris 75013, France.

Proceedings of the National Academy of Sciences of the United States of America
|January 23, 2026
PubMed
Summary
This summary is machine-generated.

Glass-former dynamics are explained by time-reparameterization softness, reconciling local mobility and configuration space complexity. Algorithms accelerate relaxation by exploiting this softness, with potential applications beyond glasses.

Keywords:
glassessampling algorithmstime reparameterization

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Computational Science

Background:

  • Ultraslow dynamics in glass-formers are traditionally explained by two competing theories: locally hindered mobility and configuration space complexity.
  • These views have been considered mutually exclusive, hindering a unified understanding of glass-forming materials.

Purpose of the Study:

  • To reconcile the competing theories explaining ultraslow dynamics in glass-formers.
  • To investigate the role of time flow and its reparameterization in glass dynamics.
  • To understand how algorithms accelerate relaxation processes in complex systems.

Main Methods:

  • Analysis of time evolution in glass-forming systems.
  • Introduction of the concept of 'time-reparameterization softness'.
  • Examination of modern algorithms designed to accelerate relaxation to equilibrium.

Main Results:

  • Demonstrated that time evolution in glass-formers exhibits 'time-reparameterization softness'.
  • Showed that local constraints reparameterize time flow, while the global landscape governs correlations.
  • Found that successful acceleration algorithms exploit this time-reparameterization softness.

Conclusions:

  • The concept of time-reparameterization softness unifies the explanations for ultraslow glass-former dynamics.
  • Modern algorithms' effectiveness stems from their ability to leverage this softness.
  • The findings may extend to constraint satisfaction problems and general algorithm optimization.