File:PhysRevX.9.021060 fig4.png

English: Upper panel: The thick green dashed line is the equilibrium locus, and the colored lines are the relaxation trajectories toward the equilibrium point (the red circle). All relaxation trajectories except the dashed red one approach equilibrium from the slow direction. The red dashed trajectory approaches equilibrium from the fast direction, and it corresponds to the strong inverse Mpemba trajectory (with bath temperature Tb=0.5 and initial temperature T∞M=0.1377). Its relaxation rate is 14.7 times faster than the other trajectories; see Fig. 5. Lower panel: A comparison between the thermodynamic limit and finite system with N=400. The dash-dot thick green line is the thermodynamic limit equilibrium line, and the dashed black line is the projection into (¯¯¯¯x1,¯¯¯¯x2) of the equilibrium line in the finite system. The projections of the relaxation trajectories for several initial temperatures are shown as thin lines, and the relaxation which corresponds to the strong Mpemba [calculated by a(TM)=0] is the thick blue dashed line. The inset shows an enlargement of the relaxation trajectories near the equilibrium. The strong Mpemba initial condition approaches equilibrium from a different direction.