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A general rate theory for resonance energy transfer is formulated toincorporate any degrees of freedom (e.g., rotation, vibration, exciton, andpolariton) as well as coherently-coupled composite states. The compact rateexpression allows us to establish useful relationships: (i) detailed balancecondition when the donor and acceptor are at the same temperature; (ii)proportionality to the overlap between donor's emission and acceptor'sabsorption spectra; (iii) scaling with the effective coherent size, i.e., thenumber of coherently coupled molecules; (iv) spatial and orientationaldependences as derived from the interaction potential. When applied tocavity-assisted vibrational energy transfer, the rate formalism provides anintuitive and quantitative explanation of intriguing phenomena such ascooperativity, resonance, and nonlinearity in the collective vibrational strongcoupling regime, as demonstrated in recent simulations.

Generalized resonance energy transfer theory: Applications to vibrational energy flow in optical cavities