Water has multiple glassy states, often called amorphous ices. Low-density (LDA) and high-density (HDA) amorphous ice are separated by a dramatic, first-order like phase transition. It has been argued that the LDA-HDA transformation connects to a first-order liquid-liquid phase transition (LLPT) above the glass transition temperature T_g. Direct experimental evidence of the LLPT is challenging to obtain, since the LLPT occurs at conditions where water rapidly crystallizes. In this work, we explore the implications of a LLPT on the pressure dependence of T_g(P) for LDA and HDA by performing computer simulations of two water models – one with a LLPT, and one without. In the absence of a LLPT, T_g(P) for all glasses nearly coincide. When there is a LLPT, different glasses exhibit dramatically different T_g(P) which are directly linked with the LLPT. Available experimental data for T_g(P) are only consistent with the scenario including a LLPT.

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