  Following experimental evidence that vibrational polaritons, formed from
collective vibrational strong coupling (VSC) in optical microcavities, can
modify ground-state reaction rates, a spate of theoretical explanations relying
on cavity-induced frictions has been proposed through the
Pollak-Grabert-H\"anggi (PGH) theory, which goes beyond transition state theory
(TST). However, by considering only a single reacting molecule coupled to
light, these works do not capture the ensemble effects present in experiments.
Moreover, the relevant light-matter coupling should have been $\sqrt{N}$ times
smaller than those used by preceding works, where $N\approx10^{6}-10^{12}$ is
the ensemble size. In this work, we explain why this distinction is significant
and can nullify effects from these cavity-induced frictions. By analytically
extending the cavity PGH model to realistic values of $N$, we show how this
model succumbs to the polariton "large $N$ problem", that is, the situation
whereby the single reacting molecule feels only a tiny $1/N$ part of the
collective light-matter interaction intensity, where $N$ is large.
