Polaritonic chemistry investigates the possible modification of chemical and photochemical reactions by means of strong light-matter coupling in optical cavities, as demonstrated in numerous experiments over the last few years. These experiments are typically interpreted in terms of the Jaynes-Cummings or Tavis-Cummings models under the assumption that the molecular ensemble is only excited by a single photon. In such a model, two polariton states compete with an overwhelming number of dark states, inhibiting polaritonic reactions entropically. We analyze the higher excitation manifolds of the Tavis-Cummings model along with a three-level system that resembles photochemical reactions. We demonstrate that allowing for more than a single excitation makes the reaction of the involved polaritons entropically more favorable.

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