Non-equilibrium origin of cavity-induced resonant modifications of chemical reactivities

In this work, we investigate the influence of light-matter coupling on reaction dynamics and equilibrium properties of a single molecule inside an optical cavity. The reactive molecule is modeled using a triple-well potential, allowing two competing reaction pathways that yield distinct products. Dynamical and equilibrium simulations are performed using the numerically exact hierarchical equations of motion approach in real- and imaginary-time formulations, respectively, both implemented with tree tensor network decomposition schemes. We consider two illustrative cases: one dominated by slow kinetics and another by ultrafast processes. Our results demonstrate that the rates of ground-state reaction pathways can be selectively enhanced when the cavity frequency is tuned into resonance with a vibrational transition directly leading to the formation of the corresponding product, even when that transition is spectroscopically dark. However, tuning cavity frequency to match an absorption-dominant transition shared across both reaction pathways does not necessarily result in pronounced rate enhancements and selectivity. Together with an additional analysis using an asymmetric double-well model, we highlight the greater complexity of underlying factors governing chemical reactivity, which extend beyond considerations of transition dipole strengths and thermal population distributions that shape linear spectroscopy. Furthermore, we found that in all scenarios, the equilibrium populations remain unchanged when the molecule is moved into the cavity, regardless of the cavity frequency. Thus, our study confirms at a fully quantum-mechanical level that cavity-induced modifications of chemical reactivities in resonant conditions arise from dynamical and non-equilibrium interactions between the cavity mode and molecular vibrations, rather than from the significant changes in equilibrium properties.