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Mpemba effect refers to the counterintuitive effect where a system which isinitially further from the final steady state equilibrates faster than anidentical system that is initially closer. The closeness to the final state isdefined in terms of a distance measure. For driven granular systems, the Mpembaeffect has been illustrated in terms of an ad-hoc measure of mean kineticenergy as the distance function. In this paper, by studying four differentdistance measures based on the mean kinetic energies as well as velocitydistribution, we show that the Mpemba effect depends on the definition of themeasures.

Mpemba effect in driven granular gases: role of distance measures