The heat capacity of matter beyond the Dulong-Petit value

We propose a simple new way to evaluate the effect of anharmonicity on a system's thermodynamic functions, such as heat capacity. In this approach, the contribution of all the potentially complicated anharmonic effects to the constant-volume heat capacity is evaluated using one parameter only: the coefficient of thermal expansion. Importantly, this approach is applicable not only to crystals, but also to glasses and viscous liquids. To support this proposal, we perform molecular dynamics simulations of several crystalline and amorphous solids as well as liquids, and find a good agreement between the results from theory and simulations. We observe an interesting non-monotonic behavior of the liquid heat capacity with a maximum, and explain this effect as being a result of competition between anharmonicity at low temperature and decreasing number of transverse modes at high temperature.