The End of Chaos at the Ideal Glass Transition
Abstract
The ideal glass transition has often been associated with the extrapolated vanishing of configurational entropy Sc, yet how this thermodynamic criterion is reflected in microscopic dynamics remains unclear. Here, we show that the vanishing of deterministic chaos quantified by the maximum Lyapunov exponent λmax provides such a dynamical signature. Using molecular dynamics simulations across diverse model glass-forming liquids in two and three dimensions, we show that λmax follows an approximate scaling λmax ∝ (T−Tλ)1/2 and extrapolates to zero at a temperature Tλ consistent with the Kauzmann temperature TK. Furthermore, we establish the quantitative relation λmax2 ∝ T Sc, directly linking chaotic dynamics to configurational entropy. By demonstrating that λmax2 ∝ σK2, where σK2 is the variance of local potential energy landscape curvature fluctuations, we connect the suppression of chaos directly to landscape geometry. These results provide a unified thermodynamic, dynamical, and geometric framework for glass formation, identifying the ideal glass transition as the endpoint of chaotic exploration of the energy landscape.
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BibTeX
@misc{wang2026chaos,
title = {{The End of Chaos at the Ideal Glass Transition}},
author = {Zi-Long Wang and Jack F. Douglas and Matteo Baggioli and Zhao-Yan Sun and Wen-Sheng Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39098},
eprint = {2610.39098},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39098},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The End of Chaos at the Ideal Glass Transition
AU - Zi-Long Wang
AU - Jack F. Douglas
AU - Matteo Baggioli
AU - Zhao-Yan Sun
AU - Wen-Sheng Xu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39098
UR - https://arxiv.org/abs/2610.39098
AB - The ideal glass transition has often been associated with the extrapolated vanishing of configurational entropy S_c, yet how this thermodynamic criterion is reflected in microscopic dynamics remains unclear. Here, we show that the vanishing of deterministic chaos quantified by the maximum Lyapunov exponent λ_max provides such a dynamical signature. Using molecular dynamics simulations across diverse model glass-forming liquids in two and three dimensions, we show that λ_max follows an approximate scaling λ_max ∝ (T−T_λ)^1/2 and extrapolates to zero at a temperature T_λ consistent with the Kauzmann temperature T_K. Furthermore, we establish the quantitative relation λ_max^2 ∝ T S_c, directly linking chaotic dynamics to configurational entropy. By demonstrating that λ_max^2 ∝ σ_K^2, where σ_K^2 is the variance of local potential energy landscape curvature fluctuations, we connect the suppression of chaos directly to landscape geometry. These results provide a unified thermodynamic, dynamical, and geometric framework for glass formation, identifying the ideal glass transition as the endpoint of chaotic exploration of the energy landscape.
ER -