help of the developed approach, we intend to demonstrate that the non-uniform density structure of the aforementioned thin film underlines the specificities of the glass transition in these systems.

Despite the fact that glass formation is generally dynamical phenomena, the main features of the vitrification transition can be captured by applying the tools of equilibrium thermodynamics. An explicit recipe that allows one to relate the glass transition temperature with the configurational entropy $S_{conf}$ of glass forming polymers has been proposed by Gibbs and DiMarzio [@Gibbs-DiMarzio]. In order to make quantitative connections between the glass transition and polymer density gradients in thin films, we intend to explore “Kauzmann paradox” or entropy crisis to occur in the nonuniform systems. Recall [@Kauzmann1948] that this paradox predicts a possible configurational entropy vanishing near the glass transition point that has been resolved in Gibbs-DiMarzio theory by the following scenario: Due to rapid precipitation of the configurational entropy upon cooling at $T_K \approx 0.77 T_g$ and crossing through the dynamical transition point, no thermodynamically stable state can exist below this point so that the system falls out of equilibrium. In non-uniform systems, similar thermodynamically unstable regions may appear in the domains of enhanced density thus causing 