Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 311 / 4 / c / iv

Local thermal stability against energy exchange with a fixed-temperature reservoir requires $C_J>0$. Since $s\ge 0$, this meansEquivalently,The lower endpoint is the divergent-heat-capacity transition. The extremal endpoint $|a|=M$ has $T_H=0$ and $C_J=0$ and is obtained only as a limiting case.