Abstract
The configurational entropy is among the key observables to characterize experimentally the formation of a glass. Physically, it quantifies the multiplicity of metastable states in which an amorphous material can be found at a given temperature, and its temperature dependence provides a major thermodynamic signature of the glass transition, which is experimentally accessible. Measurements of the configurational entropy require, however, some approximations which have often led to ambiguities and contradictory results. Here we implement a novel numerical scheme to measure the configurational entropy Sigma(T) in supercooled liquids, using a direct determination of the free energy cost to localize the system within a single metastable state at temperature T. For two prototypical glass-forming liquids, we find that Sigma(T) disappears discontinuously above a temperature T_c, which is slightly lower than the usual estimate of the onset temperature for glassy dynamics. This observation is in good agreement with theoretical expectations, but contrasts sharply with alternative numerical methods. While the temperature dependence of Sigma(T) correlates with the glass fragility, we show that the validity of the Adam-Gibbs relation (relating configurational entropy to structural relaxation time) established in earlier numerical studies is smaller than previously thought, potentially resolving an important conflict between experiments and simulations.