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.
The anomaly of specific heat in systems out of equilibrium, especially the measurement procedure dependence of specific heat, is investigated by means of free energy landscape. Introducing measurement procedure which is based on experimental method, we propose a calculation method of specific heat in systems out of equilibrium and find an abrupt change in specific heat between annealed and quenched states. For longer observation time the change in specific heat occurs at lower temperature and becomes sharper. For slower cooling of a system the transition temperature becomes lower. This cooling rate dependence of the transition temperature is consistent with experiments and thus the abrupt change in specific heat can be regarded as the glass transition which is thermally identified.
A general frame work is devised to obtain the specific heat of nonequilibrium systems described by the energy-landscape picture, where a representative point in the phase space is assumed to obey a stochastic motion which is governed by a master equation. The specific heat depends on the observation time and becomes quenched one for short observation time and annealed one for long observation time. In order to test its validity, the frame work is applied to a two-level system where the state goes back and forth between two levels stochastically. The specific heat is shown to increase from zero to the Schottky form as the observation time is increased from zero to infinity. The anomaly of specific heat at the glass transition is reproduced by a system with a model energy-landscape, where basins of the landscape form a one-dimensional array and jump rate between adjacent basins obeys a power-law distribution. It is shown that the glass transition can be understood as a transition from an annealed to a quenched system and that the glass transition temperature becomes lower when the observation time is increased.
In order to understand the behavior of thermodynamic quantities near the glass transition temperature, we put the energy landscape picture and the particle's jump motion together and calculate the specific heat of a nonequilibrium system. Taking the finite observation time into account, we study the observation time dependence of the specific heat. We assume the Einstein oscillators for the dynamics of each basin in the landscape structure of phase space and calculate the specific heat of a system with 20 basins. For a given observation time, a transition from annealed to quenched system occurs at the temperature when the time scale of jumps exceeds the observation time. The transition occurs at lower temperature and becomes sharper for longer observation time.
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