  We propose a new simple way to evaluate the effect of anharmonicity on a
system's thermodynamic functions such as heat capacity. In this approach, the
contribution of all potentially complicated anharmonic effects to
constant-volume heat capacity is evaluated by 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 results
from theory and simulations. We observe an interesting non-monotonic behavior
of liquid heat capacity with a maximum, and explain this effect as a result of
competition between anharmonicity at low temperature and decreasing number of
transverse modes at high temperature.

Statistical Mechanics