Frequency dependence and equilibration of the specific heat of glass-forming liquids

We have performed molecular dynamics simulations on a glass-forming liquid consisting of a three-dimensional binary mixture of soft spheres. We show that a peak in the specific heat versus temperature can occur because a glassy system that shows no signs of aging progresses so slowly through the energy landscape that the minimum sampling time needed to obtain accurate thermodynamic averages exceeds the observation time. We develop a systematic technique to determine the equilibrium value of the specific heat and the minimum sampling time. Below the temperature of the specific heat peak, the minimum sampling time is orders of magnitude longer than the alpha relaxation time. We find that an equilibrium system that is not undergoing structural relaxation or aging has a frequency dependent specific heat that rises as the frequency decreases. The rise occurs at frequencies corresponding to periods that are long enough for the system to sample statistically independent energies. When the period is comparable to the minimum sampling time, the frequency dependent specific heat reaches a plateau. As a result, the specific heat has a frequency dependence at frequencies orders of magnitude lower than is implied by the inverse alpha relaxation time.