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

The recent development of first-principles molecular dynamics (MD) simulations for calculating the specific heat (<i>C</i>) of liquids and glasses is reviewed. Liquid and glass states share the properties in that there is no periodicity and the atom relaxation plays a crucial role in their thermodynamic properties. For a long time, these properties have hindered the development of an appropriate theory of<i>C</i>for these states. The total energy approach based on density-functional theory (DFT) provides a universal method for calculating<i>C</i>, irrespective of the material states. However, even DFT-based MD simulations yield different values for a thermodynamic property of liquids and glasses, depending on the setup of MD simulations, aside from the convergence problem. The essential problem is atom relaxation, which affects the relationship between the energy and temperature (<i>T</i>). While temperature is determined by the equilibrium state, glasses exhibit many metastable states. These metastable states are stable within their relaxation times, leading to the difficult problem of hysteresis, which is the most profound consequence of irreversibility. Notably, irreversibility occurs even in quasistatic processes. This is the most difficult and confusing point in the thermodynamics literature. Here, a consistent treatment of equilibrium properties and in adiabatic MD simulations, which has no frictional term, is presented by considering multi-timescales. The leading principle to determine the equilibrium is provided by the second law of thermodynamics. The basic concepts and the usefulness of the total energy approach in real calculations are explained.