Free Energy Landscapes and Entropic Barriers in Glassy Systems

Abstract

Structural relaxation in supercooled liquids slows by many orders of magnitude as the glass transition is
approached, yet whether this slowdown is governed primarily by energetic barriers or by the shrinking number of
accessible configurations, that is, entropic barriers, remains actively debated. We map the free energy landscape of
a model glass-forming binary Lennard-Jones mixture (Kob-Andersen composition, N = 10,000 particles) across 22
temperatures spanning the onset temperature down to 0.85 times the mode-coupling temperature T_c, using
metadynamics-based free energy sampling along an inherent-structure-based reaction coordinate, combined with
direct configurational entropy estimates from the vibrational density of states of 500 inherent structures per
temperature. Configurational entropy density, S_conf, decreased approximately linearly with inverse temperature
above T_c but showed pronounced downward curvature below it, falling to 0.31 k_B per particle at 0.85 T_c, 42% of
its onset-temperature value. Structural relaxation time, extracted from the intermediate scattering function, followed
the Adam-Gibbs relation, log(tau) proportional to 1/(T * S_conf), with an R^2 of 0.976 across all 22 temperatures,
and deviations from this fit grew systematically only below 0.95 T_c, reaching 0.4 decades at the lowest
temperature studied. Free energy barrier heights extracted directly from the metadynamics landscape increased
from 3.1 k_BT at the onset temperature to 11.8 k_BT at 0.85 T_c, and decomposing these barriers into energetic
and entropic (T*Delta S) contributions showed that the entropic contribution grew from 38% to 61% of the total
barrier height over this range, indicating a progressive crossover from an energy-dominated to an
entropy-dominated relaxation mechanism as the glass transition is approached. A finite-size check on a subset of 8
temperatures using N = 2,000 and N = 20,000 systems found barrier heights and S_conf estimates consistent within
statistical uncertainty (differences under 5%), supporting the robustness of the reported trends. These results
provide direct, quantitative evidence that entropic barriers increasingly dominate structural relaxation in the deeply
supercooled regime, consistent with the Adam-Gibbs picture, and offer a decomposed barrier dataset that can
constrain future landscape-based theories of the glass transition.