Temperature overshooting in the Mpemba effect of frictional active matter

The traditional Mpemba effect refers to an anomalous cooling phenomenon when an initial hotter system cools down faster than an initial warm system. Such counterintuitive behavior has been confirmed and explored across phase transitions in condensed matter systems and also for colloidal particles exposed to a double-well potential. Here we predict a frictional Mpemba effect for a macroscopic body moving actively on a surface governed by Coulomb (dry) friction. For an initial high temperature, relaxation towards a cold state occurs much faster than that for an intermediate initial temperature, due to a large temperature overshooting in the latter case. This frictional Mpemba effect can be exploited to steer the motion of robots and granules.