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 $S_c$, 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 ${\lambda }_{\max }$ provides such a dynamical signature. Using molecular dynamics simulations across diverse model glass-forming liquids in two and three dimensions, we show that ${\lambda }_{\max }$ follows an approximate scaling ${\lambda }_{\max }\propto (T-T_{\lambda }{)}^{1/2}$ and extrapolates to zero at a temperature $T_{\lambda }$ consistent with the Kauzmann temperature $T_{\mathrm{K}}$. Furthermore, we establish the quantitative relation ${\lambda }_{\max }^2\propto T{S}_c$, directly linking chaotic dynamics to configurational entropy. By demonstrating that ${\lambda }_{\max }^2\propto {\sigma }_K^2$, where ${\sigma }_K^2$ 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.

arXiv comment11 pages, 16 figures