File:PhysRevX.9.021060 fig11.png

English: Lower bound for the probability of the strong Mpemba effect—the probability of the parity being positive for the direct Mpemba index [see Eq. (15)] for the case of the REM with random barriers and different system sizes L∈[4,20]. The bath temperature is kBTb=0.1. The energies are IIDs from Eq. (59) with variance σ2Elog2L and σE=1.0, and the barriers are IIDs from Eq. (60) with variance σ2Blog2L. Each point on the density plot is averaged over 2×105 realizations. We notice that the probability of the parity being positive for the direct Mpemba index seems to be converging to a finite limiting value with increasing system size.