  We prove that for various polarized varieties over $\overline{\mathbb{Q}}$,
which broadly includes K-trivial case, K-ample case, Fano case, minimal models,
certain classes of fibrations, certain metrized "minimal-like" models minimizes
the Arakelov theoretic analogue of the Mabuchi K-energy, as conjectured in
[Od15]. This is an Arakelov theoretic analogue of [H22b].
