Evolution of the ratio of the total mean kinetic energy to total random kinetic energy, calculated within the extent of the bar, (Π/T_mean(t; R < R_bar)), for the total (thin+thick) disc particles, plotted against the growth rate of the bar (dS​_bar/dt) for all thin+thick models with varying f_thick values. Left panels: evolution for the rthickS models, and the middle and right panels: evolution for models rthickE and rthickG, respectively. The thick-disc fraction (f_thick) varies from 0.1 to 1 (top to bottom), as indicated in the left-most panel of each row. The points are colour-coded by the simulation time (see the colour bar). The vertical black line denotes Π/T_mean = 5.14, which serves as a boundary for the bar instability phase, and the grey shaded region (in each sub-panel) denotes the bar-stable phase according to the OP criterion. For details, see the text.