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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...
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