Experiments in bulk water confirm the existence of two local arrangements of water molecules with different densities, but, because of inevitable freezing at low temperature T, can not ascertain whether the two arrangements separate in two phases. To avoid the freezing, new experiments measure the dynamics of water at low T on the surface of proteins, finding a crossover from a non-Arrhenius regime at high T to a regime that is approximately Arrhenius at low T. Motivated by these experiments, Kumar et al. [Phys. Rev. Lett. 100, 105701 (2008)] investigated, by Monte Carlo simulations and mean field calculations, the relation of the dynamic crossover with the coexistence of two liquid phases in a cell model for water and predict that: (i) the dynamic crossover is isochronic, i.e. the value of the crossover time τL is approximately independent of pressure P; (ii) the Arrhenius activation energy EA(P) of the low-T regime decreases upon increasing P; (iii) the temperature T^*(P) at which τ reaches a fixed macroscopic time τ^*≥ τL decreases upon increasing P; in particular, this is true also for the crossover temperature TL(P) at which τ=τL. Here, we compare these predictions with recent quasi elastic neutron scattering (QENS) experiments performed by X.-Q. Chu { et al.} on hydrated proteins at different values of P. We find that the experiments are consistent with these three predictions.
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