  We calculate the zero-temperature impurity entropy of a junction of multiple
quantum wires of interacting spinless fermions. Starting from a given
single-particle S-matrix representing a fixed point of the renormalization
group (RG) flows, we carry out fermionic perturbation theory in the bulk
interactions, with the perturbation series summed in the random phase
approximation (RPA). The results agree completely with boundary conformal field
theory (BCFT) predictions of the ground state degeneracy, and also with known
RG flows through the g-theorem.
