Dependence of the width of the glass transition interval on cooling and heating rates

In a preceding paper [J. W. P. Schmelzer, J. Chem. Phys. 136, 074512 (2012)], a general kinetic criterion of glass formation has been advanced allowing one to determine theoretically the dependence of the glass transition temperature on cooling and heating rates (or similarly on the rate of change of any appropriate control parameter determining the transition of a stable or metastable equilibrium system into a frozen-in, non-equilibrium state of the system, a glass). In the present paper, this criterion is employed in order to develop analytical expressions for the dependence of the upper and lower boundaries and of the width of the glass transition interval on the rate of change of the external control parameters. It is shown, in addition, that the width of the glass transition range is strongly correlated with the entropy production at the glass transition temperature. The analytical results are supplemented by numerical computations. Analytical results and numerical computations as well as existing experimental data are shown to be in good agreement.