  Phase stability, and the limits thereof, are a central concern of materials
thermodynamics. However, the temperature limits of equilibrium liquid stability
in chemical systems have only been widely characterized under constant
(typically atmospheric) pressure conditions, whereunder the limit is
represented by the eutectic. At higher pressures, this limit will shift in both
temperature and chemical composition, opening a wide thermodynamic parameter
space over which the absolute limit, i.e., the limit under arbitrary values of
the thermodynamic forces at play (here pressure and concentration), might
exist. In this work, we use isochoric freezing to measure this absolute limit
for the first time in several binary aqueous brines, and, nodding to the
etymology of "eutectic", we name this limit the "cenotectic" (from Greek " ",
"universal-melt"). We observe that when no solute-bearing high-pressure phases
exist, the cenotectic occurs consistently 22 +/- 2K below the 1 bar eutectic
and at approximately 213 +/- 3 MPa, suggesting domination by the liquidus
behaviors of the icy phases present. In charting the T-P evolution of each
eutectic configuration, we also encounter several unreported high-pressure
hydrates of NaHCO2, MgCl2, and NaCl, and we find that these high-pressure
phases can produce complex multi-phase configurations involving the liquid that
may remain metastable to significantly lower temperatures. We discuss the
implications of these findings for ocean worlds of our solar system and cold
ocean exoplanets; estimate thermodynamic limits on ice crust thickness and
final ocean depth ("endgame") using the cenotectic pressure; and finally
provide a generalized thermodynamic perspective on (and definition for) this
fundamental thermodynamic invariant point.
