A necessary and sufficient condition for the quantum imaginary-time Mpemba effect is that it depends only on the population ratios of excited states to the ground state.
(S55) is shorter than stopping time, then we can observe the Mpemba effect, and vice versa
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Theory of Quantum Imaginary-Time Mpemba Effect
A necessary and sufficient condition for the quantum imaginary-time Mpemba effect is that it depends only on the population ratios of excited states to the ground state.