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And yet another parameter to phase transition diagrams:

Mpemba effect: https://en.wikipedia.org/wiki/Mpemba_effect :

> The Mpemba effect is the name given to the observation that a liquid (typically water) which is initially hot can freeze faster than the same liquid which begins cold, under otherwise similar condition




From "Exploring Quantum Mpemba Effects" (2024) https://physics.aps.org/articles/v17/105 :

> Under certain conditions, warm water can freeze faster than cold water. This phenomenon was named the Mpemba effect after Erasto Mpemba, a Tanzanian high schooler who described the effect in the 1960s [1]. The phenomenon has sparked intense debates for more than two millennia and continues to do so [2]. Similar processes, in which a system relaxes to equilibrium more quickly if it is initially further away from equilibrium, are being intensely explored in the microscopic world. Now three research teams provide distinct perspectives on quantum versions of Mpemba-like effects, emphasizing the impact of strong interparticle correlations, minuscule quantum fluctuations, and initial conditions on these relaxation processes [3–5]. The teams’ findings advance quantum thermodynamics and have potential implications for technologies, ranging from information processors to engines, powered by quantum resources.




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