A Constraint-Modulated Rate Law Outperforming VFT and Its Modern Alternatives Across Canonical Glass-Forming Liquids
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914471927087104 |
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| author | Gavant, Debra S. Precker, Christian E. |
| author_facet | Gavant, Debra S. Precker, Christian E. |
| contents | A constraint-modulated rate law for viscosity in glass-forming liquids is reported. The key assumption is that each configurational state is resolved independently under its current structural constraints, rather than as a point on a predetermined free-energy surface. This approach, termed Continuous Present Actualization (CPA), requires a rate law that tracks resolution cost as it changes with temperature. The formulation, CPA + Constraint (CPA+C), introduces a temperature-dependent constraint load C(T) that quantifies how configurational access narrows as a liquid approaches the glass transition. Tested against VFT and its modern divergence-free successors MYEGA and Avramov-Milchev on canonical datasets for ortho-terphenyl, salol, and boron trioxide, CPA+C outperforms all three on four of five datasets after full AIC penalization for its two additional parameters, with margins reaching Delta-AIC = 141. On two datasets the baseline kinetic parameter vanishes, reducing the effective model to four free parameters. BIC confirms the same ranking. A smooth sigmoid variant fits equally well or better. The single exception occurs on the narrowest-range dataset, where the temperature range is too narrow for the constraint transition to separate the model from simpler alternatives. Leave-one-out cross-validation on salol (n=95) confirms that CPA+C generalizes to held-out data with mean prediction error 3x lower than the next-best model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16791 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Constraint-Modulated Rate Law Outperforming VFT and Its Modern Alternatives Across Canonical Glass-Forming Liquids Gavant, Debra S. Precker, Christian E. Materials Science Statistical Mechanics A constraint-modulated rate law for viscosity in glass-forming liquids is reported. The key assumption is that each configurational state is resolved independently under its current structural constraints, rather than as a point on a predetermined free-energy surface. This approach, termed Continuous Present Actualization (CPA), requires a rate law that tracks resolution cost as it changes with temperature. The formulation, CPA + Constraint (CPA+C), introduces a temperature-dependent constraint load C(T) that quantifies how configurational access narrows as a liquid approaches the glass transition. Tested against VFT and its modern divergence-free successors MYEGA and Avramov-Milchev on canonical datasets for ortho-terphenyl, salol, and boron trioxide, CPA+C outperforms all three on four of five datasets after full AIC penalization for its two additional parameters, with margins reaching Delta-AIC = 141. On two datasets the baseline kinetic parameter vanishes, reducing the effective model to four free parameters. BIC confirms the same ranking. A smooth sigmoid variant fits equally well or better. The single exception occurs on the narrowest-range dataset, where the temperature range is too narrow for the constraint transition to separate the model from simpler alternatives. Leave-one-out cross-validation on salol (n=95) confirms that CPA+C generalizes to held-out data with mean prediction error 3x lower than the next-best model. |
| title | A Constraint-Modulated Rate Law Outperforming VFT and Its Modern Alternatives Across Canonical Glass-Forming Liquids |
| topic | Materials Science Statistical Mechanics |
| url | https://arxiv.org/abs/2511.16791 |