Comment on “Residual entropy and structural disorder in glass: A two level model and a review of spatial and ensemble vs. temporal sampling” by A. Takada, R. Conradt, and P. Richet [J. Non-Cryst. Solids, 360, 13 (2013)]

We show that, for a two level system, the non-equilibrium (glassy state) entropy and the statistical (Gibbs) entropy – as defined by Takada et al. – are mathematically equivalent and therefore the equality between these two entropies shown by Takada et al. using simulations does not imply any new physics. In addition, we point out that the free energy of a glass, in the Takada et al. treatment, becomes less than the free energy of the liquid for all temperatures below the fictive temperature of the glass, a result that is clearly unphysical.