Negative heat capacity at phase-separation in macroscopic systems

Systems with long-range as well with short-range interactions should necessarily have a convex entropy S(E) at proper phase transitions of first order, i.e. when a separation of phases occurs. Here the microcanonical heat capacity c(E)= -\frac{(\partial S/\partial E)^2}{\partial^2S/\partial E^2} is negative. This should be observable even in macroscopic systems when energy fluctuations with the surrounding world can be sufficiently suppressed.