Any excess of vibrational energy in a molecule above its zero-point level may induce physical-chemical reactions like isomerization, dissociation, or rearrangement. The role of such vibrational energy excess is particularly relevant when a light-excited molecule transfers the photon energy to the ground state without emitting radiation. The classic example is the vision mechanism, where a complex sequence of events is triggered in the rhodopsin protein after the retinal chromophore converts photon into vibrational energy. We often say that a molecule with large vibrational energy is hot. However, if we ask what the molecule's temperature is, the question sounds odd. The fundamental thermochemistry of a canonical system tells that the environmental temperature determines the vibrational excess through ( )