Non-equilibrium relaxation in water no man's land

Determining how supercooled water relaxes in the deeply metastable regime remains a central challenge in liquid-state physics, because direct equilibrium measurements are experimentally inaccessible in the temperature range known as no man's land. To probe this regime, experiments have turned to driven approaches that repeatedly perturb the liquid while avoiding crystallization, such as nanosecond pulsed-heating procedures (PHP). Here, we use molecular dynamics simulations of TIP4P/Ice water to investigate the relaxation kinetics probed by PHP and to clarify how the relaxation times extracted from PHP relate to intrinsic isothermal relaxation and equilibrium molecular diffusion. The simulations reproduce key experimental observations, including stretched-exponential relaxation, strong kinetic asymmetry between hyperquenched water and low-density amorphous ice, and the temperature dependence of relaxation across no man's land. We show that PHP-derived relaxation times are robust descriptors of collective structural reorganization but systematically decouple from equilibrium diffusion upon cooling. This decoupling arises because PHP probes a driven relaxation pathway characterized by smaller effective activation energies than those governing molecular mobility. Consequently, PHP relaxation times exhibit a shallower temperature dependence and do not provide a reliable proxy for equilibrium molecular diffusion.