  We consider particle systems with mean-field interactions whose distribution
is invariant by translations. Under the assumption that the system seen from
its centre of mass be reversible with respect to a Gibbs measure, we establish
large deviation principles for its empirical measure at equilibrium. Our study
covers the cases of McKean-Vlasov particle systems without external potential,
and systems of rank-based interacting diffusions. Depending on the strength of
the interaction, the large deviation principles are stated in the space of
centered probability measures endowed with the Wasserstein topology of
appropriate order, or in the orbit space of the action of translations on
probability measures. An application to the study of atypical capital
distribution is detailed.
