This paper investigates the collective nature of cavity-modified chemical kinetics under vibrational strong coupling (VSC) conditions. The authors develop quantum dynamical methods to study the dynamics of chemically reacting systems in an optical cavity at finite temperatures and in the presence of a dissipative solvent. They demonstrate that in the equilibrium regime, reactivity does not exhibit altered rate behavior, but may show resonant cavity modification when the system is out of equilibrium. The results suggest experimental protocols for modifying reactivity in the collective regime and highlight features not included in the models that require further scrutiny. The study considers two model systems: Model I, a molecular system with a double-well potential and solvent interactions, and Model II, a proton transfer reaction. The authors use quantum dynamical simulations to explore the role of collective cavity coupling in the cavity-modified chemical kinetics of these systems under various initial conditions. They find that under uncorrelated initial conditions, non-equilibrium decay of state population can be significantly modified when molecules are resonantly coupled to the cavity mode. This corroborates previous works in the classical regime and those treating light-matter interactions quantum mechanically at zero temperature. Under equilibrium (correlated) initial conditions, chemical reaction rates associated with barrier crossing processes can be substantially modified only in the few-molecule limit, where other molecules provide an effective source of cavity dissipation, leading to an enhancement of chemical reaction rates in the energy diffusion-limited regime. This modification is observed when the cavity mode is resonantly coupled to molecular vibrations. However, this effect is negligible in the mean-field limit $ N \rightarrow \infty $. The study also finds that chemical reactions via direct nuclear tunneling can be modified resonantly when coupled to the cavity. These results suggest the possibility of modifying chemical dynamics by coupling molecular vibrations under non-equilibrium conditions while narrowing down the number of factors governing cavity-modified ground state chemistry. The paper is organized into sections discussing the model systems, quantum dynamics methods, numerical results, and conclusions. The authors use the hierarchical equations of motion (HEOM) approach for simulations with small N and a multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) approach for larger N. They also employ a mean-field approach for the thermodynamic limit. The results show that cavity modifications of chemical reactivity depend on the number of molecules, cavity lifetime, and photon frequency. In the thermodynamic limit, cavity modifications vanish, and the chemical reaction rate becomes independent of cavity frequency. The study highlights the importance of initial conditions and the role of collective coupling in modifying chemical reactivity under non-equilibrium scenarios.This paper investigates the collective nature of cavity-modified chemical kinetics under vibrational strong coupling (VSC) conditions. The authors develop quantum dynamical methods to study the dynamics of chemically reacting systems in an optical cavity at finite temperatures and in the presence of a dissipative solvent. They demonstrate that in the equilibrium regime, reactivity does not exhibit altered rate behavior, but may show resonant cavity modification when the system is out of equilibrium. The results suggest experimental protocols for modifying reactivity in the collective regime and highlight features not included in the models that require further scrutiny. The study considers two model systems: Model I, a molecular system with a double-well potential and solvent interactions, and Model II, a proton transfer reaction. The authors use quantum dynamical simulations to explore the role of collective cavity coupling in the cavity-modified chemical kinetics of these systems under various initial conditions. They find that under uncorrelated initial conditions, non-equilibrium decay of state population can be significantly modified when molecules are resonantly coupled to the cavity mode. This corroborates previous works in the classical regime and those treating light-matter interactions quantum mechanically at zero temperature. Under equilibrium (correlated) initial conditions, chemical reaction rates associated with barrier crossing processes can be substantially modified only in the few-molecule limit, where other molecules provide an effective source of cavity dissipation, leading to an enhancement of chemical reaction rates in the energy diffusion-limited regime. This modification is observed when the cavity mode is resonantly coupled to molecular vibrations. However, this effect is negligible in the mean-field limit $ N \rightarrow \infty $. The study also finds that chemical reactions via direct nuclear tunneling can be modified resonantly when coupled to the cavity. These results suggest the possibility of modifying chemical dynamics by coupling molecular vibrations under non-equilibrium conditions while narrowing down the number of factors governing cavity-modified ground state chemistry. The paper is organized into sections discussing the model systems, quantum dynamics methods, numerical results, and conclusions. The authors use the hierarchical equations of motion (HEOM) approach for simulations with small N and a multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) approach for larger N. They also employ a mean-field approach for the thermodynamic limit. The results show that cavity modifications of chemical reactivity depend on the number of molecules, cavity lifetime, and photon frequency. In the thermodynamic limit, cavity modifications vanish, and the chemical reaction rate becomes independent of cavity frequency. The study highlights the importance of initial conditions and the role of collective coupling in modifying chemical reactivity under non-equilibrium scenarios.