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We introduce a model of water contemplating true supercooled-liquid states that, as such, are metastable with respect to the crystalline-solid ones. Its numerical solutions reproduce from Speedy-Angell’s stability-limit picture to Poole et al.‘s metastable liquid–liquid criticality. The real existence of a liquid–liquid critical point is found to gain significant theoretical plausibility from a hitherto unnoticed analogy with the ``inversion thermodynamics’’ of Joule-Thomson gas throttling process and, by extension, with the equivalent phenomenology exhibited by black holes.

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