Summary: Let \(\mathbb U\) and \(\mathbb V\) be two sub-Markovian resolvents of kernels such that \(\mathbb V\) is \(\mathcal S\)-subordinated to \(\mathbb U\), i.e., each \(\mathbb U\)-excessive function is \(\mathbb V\)-excessive. Based on results of J. Steffens [Math. Z. 210, No. 3, 495–512 (1992; Zbl 0770.60069)], we prove that the energy functional of \(\mathbb V\) is partially induced by the one of \(\mathbb U\) by some sort of projection. As application, we solve the so-called Bochner subordination problem for entrance laws in complete generality.