Specific heat of non-equilibrium systems and glass transition

Non-equilibrium entropy of glasses formed by continuous cooling

“…As a result, ergodic statistical mechanics can be applied within each of the individual components, and the overall properties of the non-ergodic system can be computed using a suitable average over the individual components. A similar assumption has been made by Tao and coworkers [43][44][45] in their study of the heat capacity of non-equilibrium systems.…”

Free energy landscape theory of glass transition and entropy

“…The dynamics on the FEL can be mapped into a random walk equation of the tagged particle [10] which was the basis of the trapping diffusion model of the glass transition [11,12]. This approach has also been utilized in the calculation of the specific heat by Tao et al [13][14][15]. In their application, the FEL is represented by a set of deep basins and the Fokker-Planck equation (29) is replaced by the random-walk master equation among basins.…”

Fast and slow relaxations in the free energy landscape

“…In this respect, the mode coupling theory of the glass transition [2] and the replica approach to the glass transition [3] are not sufficient, since these theories fail to explain the anomaly of the specific heat observed at the glass transition point and its cooling-rate dependence. On the other hand, the free energy landscape (FEL) picture of the glass transition [4] provides a unified phenomenological understanding of the characteristics such as self-diffusion [5,6] and specific heat [7][8][9] of the glass transition. The microscopic dynamics of amorphous structure of a basin is believed to be responsible for the boson peak [10].…”