Negative heat capacities

It seems intuitive that, when energy is added to a system, its temperature will rise. Hence, the notion of negative heat capacities seems an impossibility. However, astrophysicists have argued that a star, or cluster of stars, can cool down when energy is added. Virial theorem describes the mean total kinetic energy of a system of particles bound by a potential over time. When applied to the cores of main sequence stars, as hydrogen is converted to helium by fusion, the mean molecular mass of particles increases and the core collapses. This contraction, according to virial theorem, results in a decrease in potential energy and an increase in thermal energy. Hence the core’s temperature increases as its energy falls, suggesting a negative heat capacity. A similar argument holds for clusters of atoms with negative heat capacities observed in clusters of sodium atoms.