Specific heat in nonequilibrium systems

Abstract

We propose a general framework of calculating the specific heat of the system in nonequilibrium, where the dynamics of the representative point can be separated into fast motion in a basin of energy landscape and the slow stochastic jump motion among basins. We apply this framework to gaseous hydrogen and obtain the observation time (t(obs)) dependence of the specific heat. We find that the specific heat gives the quenched and the annealed one in the limit of t(obs)-->0 and t(obs)-->infinity, respectively. We also investigate the waiting time and the observation time dependence of the specific heat and show that, for shorter waiting time, the observation time must be longer to obtain the same degree of annealing. This tendency is consistent with the observation that the glass transition temperature is higher for faster quenching.

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 specific heat is defined as the energy response to the temperature jump and the measurement process as a function of time was taken into account explicitly. They showed that the anomalous behavior of the specific heat can be understood as a transition from the annealed average at high temperatures to the quenched average at low temperatures [13,14] and that the cooling rate dependence of the glass transition temperature can be accounted by the FEL frame work [15]. Recently, non-linear energy response of glass forming materials has been analyzed on the basis of the FEL picture and it is shown that the second order ac specific heat will exhibit characteristic behaviors related to the glass transition temperature and the Vogel-Fulcher temperature [16].…”

“…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.…”

Free energy landscape approach to glass transition

“…Among several views for the glass transition, the trap model [3] provides a unified phenomenological understanding of the dynamic [4] and thermodynamic [5][6][7] anomalies at the glass transition point, and the characteristic temperature equation predicted by the trap model has been shown to agree with experiments [8,9]. It is, therefore, important to construct a microscopic foundation of the trap model, which is believed to be achieved by the free energy landscape (FEL).…”