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Vanishing of configurational entropy may not imply an ideal glass transition in randomly pinned liquids

Ozawa et. al [1] presented numerical results for the configurational entropy density, $s_c$, of a model glass-forming liquid in the presence of random pinning. The location of a "phase boundary" in the pin density ($c$) - temperature ($T$) plane, that separates an "ideal glass" phase from the supercooled liquid phase, is obtained by finding the points at which $s_c(T,c) \to 0$. According to the theoretical arguments by Cammarota et. al. [2], an ideal glass transition at which the $α$-relaxation time $τ_α$ diverges takes place when $s_c$ goes to zero. We have studied the dynamics of the same system using molecular dynamics simulations. We have calculated the time-dependence of the self intermediate scattering function, $F_s(k,t)$ at three state points in the $(c-T)$ plane where $s_c(T,c) \simeq 0$ according to Ref. [1]. It is clear from the plots that the relaxation time is finite [$τ_α\sim \mathcal{O}(10^6)]$ at these state points. Similar conclusions have been obtained in Ref.[3] where an overlap function was used to calculate $τ_α$ at these state points.