  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 $\tau $. In the density scaling regime, we argue that the decoupling
between $\tau $ and $S$ is a consequence of different values of the scaling
exponents $\gamma $ and $\gamma_S $ in the density scaling laws, $\tau = f(\rho
^\gamma /T)$ and $S = h(\rho ^{\gamma_S}/T)$, where $\rho $ and $T$ denote
density and temperature, respectively. It implies that the proper relation
between $\tau $ and $S$ requires supplementing with a density factor,
$u(\rho)$, i.e.,$\tau = g(u(\rho)w(S))$. 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 $\tau (T,\rho)$, 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 $S$.

Soft Condensed Matter