Memory control of ice growth during non-equilibrium freezing of water

Freezing of supercooled water is a classic non-equilibrium problem, yet the influence of thermal history on crystallization remains unclear. Using molecular dynamics simulations with the TIP4P/Ice model, we investigate how the initial temperature Ti shapes freezing following rapid quenching to 250 K. By monitoring the evolution of hydrogen-bonded ring structures, we find a non-monotonic dependence of the freezing time tF on Ti, with the slowest crystallization occurring near 300 K. Remarkably, this means that initially hotter water can freeze faster than cooler water, a molecular-scale analogue of the Mpemba effect. A non-stationary generalized Langevin equation framework shows that two-time memory kernels retain information about the system's thermal past, directly influencing crystallization dynamics. Structural analysis further reveals that five-membered rings act as kinetic traps, while correlations among ring types regulate the accessibility of ice-like motifs. These results uncover a molecular origin of memory-driven freezing and establish structural memory as a key driver of non-equilibrium phase transitions.