  We revisit the Hawking temperature$-$entanglement entropy criticality of the
$d$-dimensional charged AdS black hole with our attention concentrated on the
ratio $\frac{T_c \delta S_c}{Q_c}$. Comparing the results of this paper with
those of the ratio $\frac{T_c S_c}{Q_c}$, one can find both the similarities
and differences. These two ratios are independent of the characteristic length
scale $l$ and dependent on the dimension $d$. These similarities further
enhance the relation between the entanglement entropy and the
Bekenstein-Hawking entropy. However, the ratio $\frac{T_c \delta S_c}{Q_c}$
also relies on the size of the spherical entangling region. Moreover, these two
ratios take different values even under the same choices of parameters. The
differences between these two ratios can be attributed to the peculiar property
of the entanglement entropy since the research in this paper is far from the
regime where the behavior of the entanglement entropy is dominated by the
thermal entropy.
