Area scaling entropies for gravitating systems

The entropy of a spherically symmetric distribution of matter in self-equilibrium is calculated. When gravitational effects are neglected, the entropy of the system is proportional to its volume. As effects due to gravitational self-interactions become more important, the entropy acquires a correction term and is no longer purely volume scaling. In the limit that the boundary of the system approaches its event horizon, the total entropy of the system is proportional to its area. The scaling laws of the system’s thermodynamical quantities are identical to those of a black hole, even though the system does not possess an event horizon.