Aggregate Observation Drift

Let $l$ and $\tilde{l}$ be natural numbers with $l\ge2$ and $\tilde{l}\ge1$, and let $\tilde{\beta}$ be an observation-rate family on $l$ states with $\tilde{l}$ observation channels and rate bound $\tilde{B}$. The aggregate observation drift of $\tilde{\beta}$ is the function $\tilde{b}:\Delta^l\to\mathbb{R}^{\tilde{l}}$, defined on the probability simplex with values in Euclidean space, whose components are