How does entropy explain why melted ice does not spontaneously refreeze while its surroundings become hotter?

The observation that melted ice does not spontaneously refreeze while its surroundings become hotter is explained by the second law of thermodynamics, which dictates that spontaneous processes in an isolated system always proceed in the direction of increasing entropy.12

Entropy serves as a measure of a system's molecular disorder or randomness. When ice melts in a warmer environment, the thermal energy—initially concentrated in the warmer surroundings—becomes more uniformly distributed throughout the system as it reaches thermal equilibrium. This transition represents an increase in total entropy.213

While the laws of physics at the level of individual molecules are time-reversible, the second law is statistical in nature. In a macroscopic system containing an enormous number of molecules, the probability of cold molecules spontaneously gathering to form ice while the surroundings heat up is so exceedingly low that it is never observed. Thus, while not strictly impossible at the microscopic level, such an event is statistically impossible in practice, as it would require a decrease in the total entropy of the system.13