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Role of entropy in the thermodynamic evolution of the time scale of molecular dynamics near the glass transition

In this Letter, we investigate how changes in the system entropy influence the characteristic time scale of the system molecular dynamics near the glass transition. Independently of any model of thermodynamic evolution of the time scale, against some previous suppositions, we show that the system entropy $S$ is not sufficient to govern the time scale defined by structural relaxation time $τ$. In the density scaling regime, we argue that the decoupling between $τ$ and $S$ is a consequence of different values of the scaling exponents $γ$ and $γ_S $ in the density scaling laws, $τ= f(ρ^γ/T)$ and $S = h(ρ^{γ_S}/T)$, where $ρ$ and $T$ denote density and temperature, respectively. It implies that the proper relation between $τ$ and $S$ requires supplementing with a density factor, $u(ρ)$, i.e.,$τ= g(u(ρ)w(S))$. This meaningful finding additionally demonstrates that the density scaling idea can be successfully used to separate physically relevant contributions to the time scale of molecular dynamics near the glass transition. As an example, we revise the Avramov entropic model of the dependence $τ(T,ρ)$, giving evidence that its entropic basis has to be extended by the density dependence of the maximal energy barrier for structural relaxation. We also discuss the excess entropy $S_{ex}$, the density scaling of which is found to mimic the density scaling of the total system entropy $S$.