History dependence in thermodynamic properties of solids

Glasses have long been considered nonequilibrium materials. The primary reason is their history-dependent properties: the obtained properties are not uniquely determined by two state variables, temperature and volume, but are also affected by the process parameters such as cooling rates. However, closer observations reveals that this history dependence is common in solids; in crystal growth, the properties of an obtained crystal are affected by the preparation conditions through defects and metallurgical structures. The problem with the previous reasoning of history dependence lies in the lack of effort to find appropriate way of specification of the current properties, which is independent of the past history. The appropriate way is use of a full set of state variables. The guiding principle for finding them is provided by the first law of thermodynamics, which requests that the internal energy $U$ is a state function. Detailed information about the above-mentioned microstructures is needed to describe the state function $U$. This can be accomplished by specifying the time-averaged positions of all atoms that constitute the solid. Therefore, these time-averaged atom positions serve as state variables for solids. Defect states, although metastable, represent equilibrium states, while a perfect crystal is thermo-dynamically unstable. Equilibrium states can only be considered within the relaxation time. Glass is thus in equilibrium as long as its structure remains unchanged. The relaxation time is controlled by the energy barriers by which a structure is sustained, and this time restriction is inherently related to the definition of state variables. The most important property of state variables is their invariance against time averaging.