Molecular-flux-weighted reaction event size ($⟨s_i⟩=\frac{{\sum }_r{\nu }_{ir}^2{a}_r}{{\sum }_r|{\nu }_{ir}|a_r}$)

This noise-relevant event size weights absolute stoichiometric jump sizes by their molecular turnover flux. At stationarity the denominator is twice the balanced production or removal flux $v_i$, so the normalized diffusion diagonal is $D_{ii}=2⟨s_i⟩/({\tau }_i{\mu }_i)$. Fixed birth bursts of size $b$ and unit deaths give $⟨s⟩=(b+1)/2$. This quantity is not the event-count-weighted average absolute jump size.

// Target: mathematical-biology.bigb