Mpemba Effect in an Expanding Lieb-Liniger Bose gas in a hard wall box

Abstract

The Mpemba effect, broadly understood as the counterintuitive phenomenon in which a system initially farther from equilibrium relaxes faster than a system closer to equilibrium, has been widely studied in classical stochastic systems and, more recently, in quantum settings. However, its manifestation is strongly dependent on the choice of observable and the dynamical constraints of the system. In this work, we investigate the emergence of a Mpemba-type effect in the density redistribution dynamics of a strongly interacting one-dimensional Bose gas in the Tonks-Girardeau regime undergoing a sudden box expansion from length L_0 to L. By defining a physically motivated distance function based on the difference of densities between spatial regions, we provide evidence that -the relaxation dynamics of the ground and excited symmetry sectors exhibit a clear crossing in time, indicating a reversal in relaxation ordering. We emphasize that the Mpemba effect is not a universal law but rather an observable-dependent phenomenon that arises under specific dynamical conditions. In particular, we show that the interplay between initial state structure, integrability, and spatial redistribution leads to distinct relaxation pathways that enable the effect. Our results clarify common misconceptions linking the Mpemba effect to Newton's law of cooling and highlight the conditions under which such anomalous relaxation behavior can emerge in integrable quantum systems.