  The positivity of the heat capacity is the hallmark of thermal stability of
systems in thermodynamic equilibrium. We show that this property remains valid
for systems with negative derivative of energy with respect to temperature, as
happens to some system described by the microcanonical ensemble. The
demonstration rests on considering a trajectory on the Gibbs equilibrium
surface, and its projection on the entropy-energy plane. The Gibbs equilibrium
surface has the convexity property, but the projection might lack this
property, leading to a negative derivative of energy with respect to
temperature.
