  The effective central charge (denoted by $c_{\text{eff}}$) is a measure of
entanglement through a conformal interface, while the transmission coefficient
(encoded in the coefficient $c_{LR}$ of the two-point function of the
energy-momentum tensor across the interface) is a measure of energy
transmission through the interface. It has been pointed out that these two are
generally different. In this article, we propose the inequalities, $0 \leq
c_{LR} \leq c_{\text{eff}} \leq \min (c_L,c_R)$. They have the simple but
important implication that the amount of energy transmission can never exceed
the amount of information transmission. We verify them using the AdS/CFT
correspondence, using the perturbation method, and in examples beyond
holography. We also show that these inequalities are sharp by constructing a
class of interfaces that saturate them.
