  The production of the $X(3872)$ particle in heavy-ion collisions has been
contemplated as an alternative probe of its internal structure. To investigate
this conjecture, we perform transport calculations of the $X(3872)$ through the
fireball formed in nuclear collisions at the LHC. Within a kinetic-rate
equation approach as previously used for charmonia, the formation and
dissociation of the $X(3872)$ is controlled by two transport parameters, i.e.,
its inelastic reaction rate and thermal-equilibrium limit in the evolving hot
QCD medium. While the equilibrium limit is controlled by the charm production
cross section in primordial nucleon-nucleon collisions (together with the
spectra of charm states in the medium), the structure information is encoded in
the reaction rate. We study how different scenarios for the rate affect the
centrality dependence and transverse-momentum ($p_T$) spectra of the $X(3872)$.
Larger reaction rates associated with the loosely bound molecule structure
imply that it is formed later in the fireball evolution than the tetraquark and
thus its final yields are generally smaller by around a factor of two, which is
qualitatively different from most coalescence model calculations to date. The
$p_T$ spectra provide further information as the later decoupling time within
the molecular scenario leads to harder spectra caused by the blue-shift from
the expanding fireball.
