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