Thermodynamics in the region of glass transition

Since glasses are inherently in a non-equilibrium state around Tg, thermodynamic formulation relevant for this region has to include one important additional feature and that is a time scale. Even in laboratory time scales profound changes in properties can occur. It is the existence of this time scale, which led to the definition of a fictive temperature by Tool (Tool and Eichlin, 1931 Tool, 1946). If we call this reference or fictive temperature as 7/ (which is more accurately written as T/J) since it is time-dependent), then the Gibb s free energy of a glass can be described in terms of three parameters, T, P and Tf. Also the heat balance equation in 

Since total entropy S is equal to Sc + Sc and from the second law of thermodynamics, TdS dQ, we have 

Since Tf is also a function of T and P, as both the entropy terms are, one can calculate the heat capacity of a glass in the region of glass transition as 

Nieuwenhuizen (2000) has shown that one of the Ehrenfest relations becomes 

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