We use the recently-proposed emph{compressible cell} Ising-like model [Phys. Rev. Lett. textbf{120}, 120603 (2018)] to estimate the ratio between thermal expansivity and specific heat (the Gruneisen parameter $Gamma$) in supercooled water. Near the critical pressure and temperature, $Gamma$ increases. The $Gamma$ value diverges near the pressure-induced finite-$T$ critical end-point [Phys. Rev. Lett. textbf{104}, 245701 (2010)] and quantum critical points [Phys. Rev. Lett. textbf{91}, 066404 (2003)], which indicates that two energy scales are governing the system. This enhanced behavior of $Gamma$ is caused by the coexistence of high- and low-density liquids [Science textbf{358}, 1543 (2017)]. Our findings support the proposed liquid-liquid critical point in supercooled water in the No-Mans Land regime, and indicates possible applications of this model to other systems.
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