A study, based upon the Gibbs free energy, is made of the thermodynamical behaviour of dissipative and memory‐dependent materials. The creep‐function mechanical properties involved are generalizations of the usual volumetric compressibility, the coefficient of thermal expansion, and the specific heat at constant pressure. It is found that under a certain special equilibrium condition, a transition behaviour occurs in the material whereby the mechanical and thermal properties change with time. The criterion for its occurrence is that of a certain proportionality between the volumetric, thermal expansion and specific‐heat creep functions. This criterion is interpreted as that of the glass‐transition temperature, the resulting forms bear some resemblance to those of an Ehrenfest second‐order transition. However, the similarity is only superficial since herein full account is taken of time‐dependent memory effects. Attention is given to the relationship of the present work to previous studies, which did not specifically account for time‐dependent memory effects, but which did account for some type of irreversible process through the use of “internal variables.” The application of the present criterion suggests a specific and new means of unambiguously determining the glass‐transition temperature for polymers. Also, the thermodynamic study indicates some avenues of research into the underlying kinetic causes of glass‐transition behaviour.