The existence of exotic systems with anomalous negative heat capacities have been claimed in the recent literature. Those negative heat capacities are responsible for all kind of peculiar thermodynamic behaviors, such as the temperature of the anomalous system being reduced when the system is heated. Close inspection shows that negative heat capacities have not been measured, neither do exist. Classic thermodynamic stability theory states that heat capacities have to be positive [1,2]. For a system in thermal contact with a larger system, the second order virtual variation in entropy around an equilibrium state is \[ \delta^2 S = - \frac{C_V (\delta T)^2}{T^2} \lt 0 , \] with heat capacity at constant volume \[ C_V = \left( \frac{\partial E}{\partial T} \right)_V , \] and the negative sign required by stability implying that \( C_V \gt 0 \). Recall that the quantities used in thermodynamics are averages over microscopic realizations. For instance, the thermodynamic internal ene