  We perform stringent tests of thermodynamic theories of the glass transition
over the experimentally relevant temperature regime for several simulated
glass-formers. The swap Monte Carlo algorithm is used to estimate the
configurational entropy and static point-to-set lengthscale, and careful
extrapolations are used for the relaxation times. We first quantify the
relation between configurational entropy and the point-to-set lengthscale in
two and three dimensions. We then show that the Adam-Gibbs relation is
generally violated in simulated models for the experimentally relevant time
window. Collecting experimental data for several supercooled molecular liquids,
we show that the same trends are observed experimentally. Deviations from the
Adam-Gibbs relation remain compatible with random first order transition
theory, and may account for the reported discrepancies between Kauzmann and
Vogel-Fulcher-Tammann temperatures. Alternatively, they may also indicate that
even near $T_g$ thermodynamics is not the only driving force for slow dynamics.

Statistical Mechanics;Soft Condensed Matter