  Conduction electrons coupled to a mesoscopic superconducting island hosting
Majorana bound states have been shown to display a topological Kondo effect
with robust non-Fermi liquid correlations. With $M$ bound states coupled to $M$
leads, this is an SO($M$) Kondo problem, with the asymptotic high and low
energy theories known from bosonization and conformal field theory studies.
Here we complement these approaches by analyzing the Bethe ansatz equations
describing the exact solution of these models at all energy scales. We apply
our findings to obtain nonperturbative results on the thermodynamics of
$M\rightarrow M-2$ crossovers induced by tunnel couplings between adjacent
Majorana bound states.
