  Boundary S matrices for the boundary tricritical Ising field theory (TIM),
both with and without supersymmetry, have previously been proposed. Here we
provide support for these S matrices by showing that the corresponding boundary
entropies are consistent with the expected boundary flows. We develop the
fusion procedure for boundary RSOS models, with which we derive exact inversion
identities for the TIM. We confirm the TBA description of nonsupersymmetric
boundary flows of Lesage et al., and we obtain corresponding descriptions of
supersymmetric boundary flows.
