  Microcavities have been shown to influence the reactivity of molecular
ensembles by strong coupling of molecular vibrations to quantized cavity modes.
In quantum mechanical treatments of such scenarios, frequently idealized models
with single molecules and scaled, effective molecule-cavity interactions or
alternatively ensemble models with simplified model Hamiltonians are used. In
this work, we go beyond these models by applying an ensemble variant of the
Pauli-Fierz Hamiltonian for vibro-polaritonic chemistry and numerically solve
the underlying time-dependent Schr\"odinger equation to study the
cavity-induced quantum dynamics in an ensemble of thioacetylacetone (TAA)
molecules undergoing hydrogen transfer under vibrational strong coupling (VSC)
conditions. Beginning with a single molecule coupled to a single cavity mode,
we show that the cavity indeed enforces hydrogen transfer from an enol to an
enethiol configuration with transfer rates significantly increasing with
light-matter interaction strength. This positive effect of the cavity on
reaction rates is different from several other systems studied so far, where a
retarding effect of the cavity on rates was found. It is argued that the cavity
``catalyzes'' the reaction by transfer of virtual photons to the molecule. The
same concept applies to ensembles with up to $N=20$ TAA molecules coupled to a
single cavity mode, where an additional, significant, ensemble-induced
collective isomerization rate enhancement is found. The latter is traced back
to complex entanglement dynamics of the ensemble, which we quantify by means of
von Neumann-entropies. A non-trivial dependence of the dynamics on ensemble
size is found, clearly beyond scaled single-molecule models, which we interpret
as transition from a multi-mode Rabi to a system-bath-type regime as $N$
increases.
