Extend the unified temperature-folding framework beyond first-order phase transitions

Determine whether the unified analytical framework based on the folding structure of the black-hole temperature function can be extended to other types of phase transitions, and whether additional analytical frameworks can likewise be reduced to that folding structure.

Background

The paper unifies global topology, thermodynamic geometry, complex analysis, and local geometric analysis for black hole first-order phase transitions by tracing their characteristic quantities to the extremal-point structure, or folding structure, of the temperature function.

The authors identify broader unresolved directions: whether the same framework applies to phase transitions other than black hole first-order transitions, and whether further analytical frameworks not included in the present four-framework construction can be understood through the same temperature-folding structure.

References

For example, can it be extended to other types of phase transitions, and do there exist undiscovered analytical frameworks that can likewise be reduced to the folding structure of the temperature function?

— Thermodynamic geometry as the missing link: toward a unified framework for black hole first-order phase transitions  (2609.31144 - Zhang et al., 25 Sep 2026) in Section 6, “Further comments and conclusions”