  We investigate the possibility of characterizing the different thermalization
pathways through a large-deviation approach. Specifically, we consider clean,
disordered and quasi-periodic harmonic chains under energy and
momentum-conserving noise. For their associated master equations, describing
the dynamics of normal modes energies, we compute the fluctuations of activity
and dynamical entropy in the corresponding biased ensembles. First-order
dynamical phase transition are found that originates from different activity
regions in action space. At the transitions, the steady-state in the biased
ensembles changes from extended to localized, yielding a kind of condensation
in normal-modes space. For the disordered and quasi-periodic models, we argue
that the phase-diagram has a critical point at a finite value of the disorder
or potential strength.
