Thermodynamic Stability of Causal Diamonds*

It has been shown that causal diamonds can be viewed as local gravitational thermodynamic systems. In particular, they obey a first law, and interestingly have negative temperature. The equilibrium state of the diamond is a state in which the geometry is maximally symmetric and the quantum fields are at their vacuum state. The total entropy of such a state is extremal. Second order variations of entropy and also the diamond’s free energy is considered in this work, in order to find whether the equilibrium state is stable. The answer seems to be affirmative.