[Noughmad]

The simple answer is that the cool system has a very uniform temperature (because it's been at that temperature for a long time), while the hot system that's cooling down is doing so with large spatial variations of temperature. In other words, all the water in the initially cool system is at 10°C, but the initially hot system has pockets of 5°C and pockets of 15°C.

It doesn't have to "learn" anything in order for there to be a substantial difference.

[ephbit]

These temperature gradients obviously lead to convection.

Stronger convection means greater heat transfer, thus greater rate of cooling down.

But it'd be surprising if the inertia of the convection of the initially hot system didn't just gradually decline (because of friction) to almost exactly (little bit greater) the same level of convection (which the initially cool system had in the beginning) when it reaches the same average temperature.

[londons_explore]

Water currents can last a surprisingly long time. Pour one liquid into another of a slightly different color and the swirling mixing process can go on for minutes at least. Perhaps hours in the right circumstances.

[infogulch]

Interesting theory for a specific mechanism: "local temperature difference-induced convective cooling". Could be falsified by giving both initially-hot and initially-cold samples a stir rod, expecting the cooling performance of the initially-cold sample to improve to match the initially-hot sample.

[waterhouse]

Ho ho, guess what?

> The Scottish scientist Joseph Black investigated a special case of this phenomenon comparing previously-boiled with unboiled water; the previously-boiled water froze more quickly. Evaporation was controlled for. He discussed the influence of stirring on the results of the experiment, noting that stirring the unboiled water led to it freezing at the same time as the previously-boiled water, and also noted that stirring the very-cold unboiled water led to immediate freezing. https://en.wikipedia.org/wiki/Mpemba_effect

I'm surprised the article didn't mention this.

[infogulch]

Wow! I guess that's the final answer then. Maybe to seal it, devise the inverse experiment where you somehow inhibit normal convection in boiled water and expect to see it take as long as the cold water.

Very interesting!