  We discuss how to extend the impurity entropy to systems with boundary
interactions depending on zero-mode real fermion operators (Majorana modes as
well as Klein factors). As specific applications of our method, we consider a
junction between N interacting quantum wires and a topological superconductor,
as well as a Y-junction of three spinless interacting quantum wires. In
addition we find a remarkable correspondence between the N=2 topological
superconductor junction and the Y-junction. On one hand, this allows us to
determine the range of the system parameters in which a stable phase of the N=2
junction is realized as a nontrivial, finite-coupling fixed point corresponding
to the M-fixed point in the phase diagram of the Y-junction. On the other hand,
it enables us to show the occurrence of a novel "planar" finite-coupling fixed
point in the phase diagram of the Y-junction. Eventually, we discuss how to set
the system's parameters to realize the correspondence.
