Mpemba effect in systems with boundary coupling*

The Mpemba effect is a counterintuitive phenomenon where under proper conditions, a hot system cools down faster than an initially cold system when quenching both to an even colder bath. The nonequilibrium thermodynamics framework provides a comprehensive high-level characterization of this phenomenon, which has been observed in systems including water, magnetic alloys, polymers, granular gasses and colloidal systems. However, in most experiments the system is coupled to the heath-bath only through its boundaries, whereas the theoretical studies presented so far assumed bulk coupling, hindering the adequacy of this description for large sized systems.
To further close the gap between the theoretical framework and the experiments, we study a 1D antiferromagnet nearest neighbor interacting Ising periodic chain in which only part of the system is coupled to the heath-bath. We show that such a system exhibits an extremely rich variety of anomalous relaxations. This ultimately proves the validity of this theoretical characterization of the effect also in a boundary coupling setup.