In quest of reaching minimum enthalpy

The formation of glasses is inherently a non-equilibrium process in which the final state depends on the thermal history. In variable-cooling-rate glass annealing, where identifying the precise moment of glass transition becomes ambiguous, the concept of a glass transition interval has been put forward. By formulating glass formation during non-steady cooling from the liquid to the glassy state as a time-constrained enthalpy minimization, we derive a simple explicit solution for the optimal cooling rate within the framework of a single-relaxation-time model. By exploiting a one-to-one correspondence between enthalpy and fictive temperature, we demonstrate that minimizing the final enthalpy is equivalent to minimizing the limiting fictive temperature, independent of the cooling path. The optimal solution acquires a physical interpretation via the phenomenological glass transition criteria, normalized using a conventional standard cooling rate. The glass formation criterion standardization highlights the constant-cooling-rate dependence of the glass transition temperature as experimental evidence for an Arrhenius-type structural relaxation time in the glass transition region. Our theoretical results, including suboptimal cooling protocols and a universal scaling of the differential scanning calorimetry heat capacity curve, establish a basis for the rational design and optimization of glass annealing and suggest a reinterpretation of experimental measurements of the glass transition region.