  For a small fraction of hot CO2 molecules immersed in a liquid-phase CO2
thermal bath, classical cavity molecular dynamics simulations show that forming
collective vibrational strong coupling (VSC) between the C=O asymmetric stretch
of CO2 molecules and a cavity mode accelerates hot-molecule relaxation. The
physical mechanism underlying this acceleration is the fact that polaritons,
especially the lower polariton, can be transiently excited during the
nonequilibrium process, which facilitates intermolecular vibrational energy
transfer. The VSC effects on these rates (i) resonantly depend on the cavity
mode detuning, (ii) cooperatively depend on molecular concentration or Rabi
splitting, and (iii) collectively scale with the number of hot molecules, which
is similar to Dicke's superradiance. For larger cavity volumes, due to a
balance between this superradiant-like behavior and a smaller light-matter
coupling, the total VSC effect on relaxation rates can scale slower than $1/N$,
and the average VSC effect per molecule can remain meaningful for up to $N
\sim10^4$ molecules forming VSC. Moreover, we find that the transiently excited
lower polariton prefers to relax by transferring its energy to the tail of the
molecular energy distribution rather than equally distributing it to all
thermal molecules. Finally, we highlight the similarities of parameter
dependence between the current finding with VSC catalysis observed in
Fabry-Perot microcavities.
