  For algebro-geometric study of J-stability, a variant of K-stability, we
prove a decomposition formula of non-archimedean $\mathcal{J}$-energy of
$n$-dimensional varieties into $n$-dimensional intersection numbers rather than
$(n+1)$-dimensional ones, and show the equivalence of slope
$\mathrm{J}^H$-(semi)stability and $\mathrm{J}^H$-(semi)stability for surfaces
when $H$ is pseudoeffective. Among other applications, we also give a purely
algebro-geometric proof of a uniform K-stability of minimal surfaces due to
[23], and provides examples which are J-stable (resp., K-stable) but not
uniformly J-stable (resp., uniformly K-stable).
