The effective central charge (denoted by c_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 Letter, we propose the inequalities, $0lec_LRlec_efflemin(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.
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