  The purpose of this note, as a compendium, is to extend the results on
entropic convergence and the linearized limit for the Boltzmann equation
(without external force) in \cite{Levermore} by Levermore to the case of the
Boltzmann equation with external force. More specifically, starting from the
Boltzmann equation with an external force introduced in \cite{DL16} by
Ars\'{e}nio and Saint-Raymond, we find conditions on the force, to maintain the
result in \cite{Levermore} (as an important application of the theory of
DiPerna-Lions renormalized solutions) about the validity of the linearization
approximation when the initial datum approaches a global Maxwellian.
