# The stability-limit conjecture revisited

## TL;DR

This paper reevaluates the stability-limit conjecture for supercooled water, demonstrating its thermodynamic plausibility within models that include both liquid-gas and liquid-liquid phase transitions, and clarifies related unusual behaviors.

## Contribution

It shows that the stability-limit conjecture can be thermodynamically consistent if a binodal terminates on a spinodal away from a critical point, expanding understanding of supercooled water behavior.

## Key findings

- The SLC is thermodynamically permissible with multiple phase transitions.
- A binodal can terminate on a spinodal without a critical point.
- Clarification of the 'critical-point-free' scenario in supercooled liquids.

## Abstract

The stability-limit conjecture (SLC) proposes that the liquid spinodal of water returns to positive pressure in the supercooled region, and that the apparent divergence of water's thermodynamic response functions as temperature decreases are explained by the approach to this reentrant spinodal. Subsequently, it has been argued that the predictions of the SLC are inconsistent with general thermodynamic principles. Here we reconsider the thermodynamic viability of the SLC by examining a model equation of state for water first studied to clarify the relationship of the SLC to the proposed liquid-liquid phase transition in supercooled water. By demonstrating that a binodal may terminate on a spinodal at a point that is not a critical point, we show that the SLC is thermodynamically permissible in a system that has both a liquid-gas and a liquid-liquid phase transition. We also describe and clarify other unusual thermodynamic behavior that may arise in such a system, particularly that associated with the so-called "critical-point-free" scenario for a liquid-liquid phase transition, which may apply to the case of liquid Si.