What is Spread capture, adverse-selection cost, inventory P&L?

For a fill of side $s$, quantity $q$ and price $p$ at time $t$, with reference price $m$, horizon $H$ and the end of the period $T$: the spread capture is $sq\,(m(t) - p)$; the adverse-selection cost is $sq\,(m(t + H) - m(t))$; the inventory P&L is $sq\,(m(T) - m(t + H))$. Summed over fills, with fees, the three add up to the P&L of the fills with the final position marked at $m(T)$.