I am now interested in the local rate of transitions at a particular state. I expect most states to be represented by unbranched nodes (Fig. ) and I can therefore write Eq. 1b as a simple differential equation (Eq. 5a). Such a simplification should only be valid at sufficiently high energy levels away from the ground state. It is now convenient to write 𝑛(𝑞) as a difference to its thermally equilibrated value, ∆𝑛(𝑞), see Eqs. 5b and 5c.