  We propose a numerical technique to compute the equilibrium free energy of
glasses that cannot be prepared quasi-reversibly. For such systems, standard
techniques for estimating the free energy by extrapolation, cannot be used.
Instead, we use a procedure that samples the equilibrium partition function of
the basins of attraction of the different inherent structures (local potential
energy minima) of the system. If all relevant inherent structures could be
adequately sampled in the (supercooled) liquid phase, our approach would be
rigorous. In any finite simulation, we will miss the lower-energy inherent
structures that become dominant at very low temperatures. We find that our free
energy estimates for a Kob-Andersen glass are lower than those obtained by very
slow cooling, even at temperatures down to one third of the glass transition
temperature. The current approach could be applied to compute the chemical
potential of ultra-stable glassy materials, and should enable the estimation of
their solubility.
