  A general rate theory for resonance energy transfer is formulated to
incorporate any degrees of freedom (e.g., rotation, vibration, exciton, and
polariton) as well as coherently-coupled composite states. The compact rate
expression allows us to establish useful relationships: (i) detailed balance
condition when the donor and acceptor are at the same temperature; (ii)
proportionality to the overlap between donor's emission and acceptor's
absorption spectra; (iii) scaling with the effective coherent size, i.e., the
number of coherently coupled molecules; (iv) spatial and orientational
dependences as derived from the interaction potential. When applied to
cavity-assisted vibrational energy transfer, the rate formalism provides an
intuitive and quantitative explanation of intriguing phenomena such as
cooperativity, resonance, and nonlinearity in the collective vibrational strong
coupling regime, as demonstrated in recent simulations.
