Analogue of the Mpemba effect in classical mechanics

Abstract

The name "Mpemba effect" was given to the finding that "If two systems are cooled, the water that starts hotter may freeze first", confirmed by numerous of observations. Now this paradoxical state-ment obtained a more general form "the state that is initially more distant from its equilibrium state comes to this state earlier". Though seemingly violating the fundamental laws of physical chemistry, this effect has been experimentally demonstrated for aqueous and various other systems, up to quan-tum dots. It was widely discussed in the American Journal of Physics, Nature, and other highly reputa-ble journals, but the fundamental physical mechanism(s) underlying this effect remained elusive. Here I describe a simple mechanical system demonstrating the Mpemba effect ("the state that is initially more distant from its equilibrium state comes to this state earlier"), and show what physical mechanism causes this effect in this system.