File:PhysRevX.9.021060 fig9.png

English: The probability for the odd direct Mpemba index for a particular random draw of L=15 energy levels obtained two independent ways: analytically by averaging over the isotropic ensemble (solid line) and numerically by averaging over random barriers (points). The energy level realization is drawn from a Gaussian distribution with zero mean and standard deviation 1.5. Each point corresponds to the average of 4000 barrier realizations taken from a truncated Gaussian distribution with zero mean and standard deviation 15 (the Gaussian is truncated to have only positive Bij values). The solid line represents the analytical result for the isotropic ensemble Eq. (50).