When computing the free energy associated with each polaritonic state, it is possible to have the "lower" polariton lying above the dark states because of its lower entropic contribution to its free energy as schematically depicted in Fig. . Fig. presents numerical results for g c = 50 cm -1 and 75 cm -1 represented by red and cyan dots respectively, with N = 2000 and a Gaussian disorder with a standard deviation of 25 cm -1 at T = 300 K. In both cases, a substantial number of dark states lie above the dashed solid line that is represented as E Dark -E LP = T (S Dark -S LP ). The reordering between dark states and the lower polariton occurs for T (S Dark -S LP ) > E Dark -E LP . Therefore such dark states lie below the "lower" polariton when considering free energy.