The total energy approach for calculating the specific heat of liquids and glasses

The recent development of the calculation of specific heat ($C$) of liquids and glasses by first-principles molecular dynamics (MD) simulations is reviewed. Liquid and glass states have common properties in that there is no periodicity and the atom relaxation has an important role in their thermodynamic properties. These properties have, for a long time, hindered the construction of an appropriate theory of $C$ for these states. The total energy approach based on the density-functional theory (DFT) provides a universal method to calculate $C$, irrespective of the material states. However, aside from the convergence problem, even DFT-based MD simulations give different values for a thermodynamic property of liquids and glasses, depending on the setup of MD simulations. The essential problem is atom relaxation, which affects the relationship between the energy and temperature $T$. The temperature is determined by the equilibrium state, but there are many metastable states for glasses. Metastable states are stable within their relaxation times. We encounter the difficult problem of hysteresis, which is the most profound consequence of irreversibility. Irreversibility occurs even for quasistatic processes. This is the most difficult and confusing point in the thermodynamics literature. Here, a consistent treatment of both equilibrium properties and irreversibility in adiabatic MD simulations, which has no frictional term, is given by taking multi-timescales into account. A leading principle to determine the equilibrium is provided by the second law of thermodynamics. The basic ideas and the usefulness of the total energy approach in real calculations are presented.