Specific entropy and the sign of the energy

The second law in the context of black holes restricts the specific entropy of an arbitrary system of given size; this limitation cannot be avoided by appealing to the buoyant effects of black-hole radiation. Quantum statistics sets a similar bound for field systems with positive ground energies. Examples of fields with negative vacuum energies have recently been adduced against the bound on specific entropy. We stress that the bound still holds if applied to a complete system.