Abstract A thermodynamic theory for an isolated system in a cavity consisting of two subsystems with intrinsic heat capacities of opposite sign has been developed. The usual heat capacity at constant volume CV given as a linear sum of two subsystems’ heat capacities, expresses the concavity of the equilibrium entropy of the system, but is not a good indicator of system stability. The mean square amplitudes of the fluctuations of the subsystems are unequivocally related to a heat capacity C'V, newly defined as the harmonic sum of those of the subsystems. A change in the system from stable to unstable occurs when C'V changes from +∞ to –∞, or equivalently when the equilibrium entropy changes from convex (CV < 0) to concave (CV > 0) through a cusp, but not through an inflection point. The thermodynamic properties of a Schwarzschild black hole immersed in black-body radiation in a cavity have been worked out in detail.