  This paper gives a free entropy theoretic perspective on amenable absorption
results for free products of tracial von Neumann algebras. In particular, we
give the first free entropy proof of Popa's famous result that the generator
MASA in a free group factor is maximal amenable, and we partially recover
Houdayer's results on amenable absorption and Gamma stability. Moreover, we
give a unified approach to all these results using $1$-bounded entropy. We show
that if $\mathcal{M} = \mathcal{P} * \mathcal{Q}$, then $\mathcal{P}$ absorbs
any subalgebra of $\mathcal{M}$ that intersects it diffusely and that has
$1$-bounded entropy zero (which includes amenable and property Gamma algebras
as well as many others). In fact, for a subalgebra $\mathcal{P} \leq
\mathcal{M}$ to have this absorption property, it suffices for $\mathcal{M}$ to
admit random matrix models that have exponential concentration of measure and
that "simulate" the conditional expectation onto $\mathcal{P}$.
