"statistical physics" in this case is called "thermodynamics" (the first scientific application of statistics). Basically it's very similar to a vapor distillation process; there's always some mixing of the components between phases due to entropy, even though there's an energy gradient driving each component towards a phase. However, you can get asymptotically close to full purification using multiple steps.

There's also a tradeoff between how much you recover and how pure the final product is. Mineral processors describe this as a "grade recovery curve" [1].

This is definitely purely of historical interest. At best, it's basically saying "medieval Africans' purification process was significantly better than medieval Europeans' process". Either of these methods is handily beat by gold cyanidation and other modern processes.

https://upload.wikimedia.org/wikipedia/en/8/85/Shifts_in_Rec...