How Fast Does a Glass Forget? LandscapeConnectivity, Not Barrier Height, Sets the Rateof Memory Erasure under Repeated ThermalCycling
4 affiliations
- 1LAAS-CNRS
- 2Université de Toulouse, CNRS
- 3Faculté des Sciences Ben M’Sik
- 4Université Hassan II de Casablanca
Abstract
How fast a glass forgets its thermal history under repeated thermal cycling could be set by the height of its slowest barrier, by the number of relaxation channels it has, or by how those channels interconnect.We separate the three.Multi-scan calorimetry and industrial annealing and tempering all repeat a cooling and heating ramp many times, yet discrete-state models of thermal history have so far been driven through only a single pass.We build a 40-level master equation directly from the inherent-structure distribution of embedded-atom molecular dynamics of Cu 50 Zr 50 , so that level energies and degeneracies are measured rather than chosen, and drive it through many non-reset cycles.Because the dynamics are linear, one cycle is an exact map P n+1 = M P n whose second eigenvalue λ 2 is the fraction of the previous cycle's memory surviving one further cycle.It is the cycle-to-cycle counterpart of a structural relaxation time: -1/ ln λ 2 is the number of cycles needed to forget by 1/e, and dividing the cycle duration by -ln λ 2 converts it to seconds.In the atomistic system λ 2 = 0.73 to 0.81, that is 3 to 5 cycles, or 3.5 to 5.3 ns.Holding every barrier fixed and varying only connectivity, the cycles needed to forget fall by a factor of 77 without saturating, and one graph invariant, the effective resistance between the states a cycle must exchange population between, predicts the rate: |µ 2 | ∝ R -1.06 eff across six topologies and six turnaround temperatures (r = -0.996).A closed form, λ 2 = exp[-∮︁ |µ slow | dt], reproduces this to 0.07%.Cycling the atomistic system itself places the measured rate on the k = 3 prediction and excludes landscapes as densely connected as k ≥ 4. Connectivity, not the number of relaxation channels, sets how fast a thermally cycled glass forgets.
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BibTeX
@misc{jabraoui2026fast,
title = {{How Fast Does a Glass Forget? LandscapeConnectivity, Not Barrier Height, Sets the Rateof Memory Erasure under Repeated ThermalCycling}},
author = {Hicham Jabraoui and Said Ouaskit},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15007414/v2},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15007414/v2},
note = {CC BY},
}
RIS
TY - UNPB
TI - How Fast Does a Glass Forget? LandscapeConnectivity, Not Barrier Height, Sets the Rateof Memory Erasure under Repeated ThermalCycling
AU - Hicham Jabraoui
AU - Said Ouaskit
PY - 2026
DA - 2026/09/23
PB - ChemRxiv
DO - 10.26434/chemrxiv.15007414/v2
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15007414/v2
AB - How fast a glass forgets its thermal history under repeated thermal cycling could be set by the height of its slowest barrier, by the number of relaxation channels it has, or by how those channels interconnect.We separate the three.Multi-scan calorimetry and industrial annealing and tempering all repeat a cooling and heating ramp many times, yet discrete-state models of thermal history have so far been driven through only a single pass.We build a 40-level master equation directly from the inherent-structure distribution of embedded-atom molecular dynamics of Cu 50 Zr 50 , so that level energies and degeneracies are measured rather than chosen, and drive it through many non-reset cycles.Because the dynamics are linear, one cycle is an exact map P n+1 = M P n whose second eigenvalue λ 2 is the fraction of the previous cycle's memory surviving one further cycle.It is the cycle-to-cycle counterpart of a structural relaxation time: -1/ ln λ 2 is the number of cycles needed to forget by 1/e, and dividing the cycle duration by -ln λ 2 converts it to seconds.In the atomistic system λ 2 = 0.73 to 0.81, that is 3 to 5 cycles, or 3.5 to 5.3 ns.Holding every barrier fixed and varying only connectivity, the cycles needed to forget fall by a factor of 77 without saturating, and one graph invariant, the effective resistance between the states a cycle must exchange population between, predicts the rate: |µ 2 | ∝ R -1.06 eff across six topologies and six turnaround temperatures (r = -0.996).A closed form, λ 2 = exp[-∮︁ |µ slow | dt], reproduces this to 0.07%.Cycling the atomistic system itself places the measured rate on the k = 3 prediction and excludes landscapes as densely connected as k ≥ 4. Connectivity, not the number of relaxation channels, sets how fast a thermally cycled glass forgets.
ER -