  We consider some of the main notions of Gibbs measures on subshifts
introduced by different communities, such as dynamical systems, probability,
operator algebras, and mathematical physics. For potentials with $d$-summable
variation, we prove that several of the definitions considered by these
communities are equivalent. In particular, when the subshift is of finite type
(SFT), we show that all definitions coincide. In addition, we introduced a
groupoid approach to describe some Gibbs measures, allowing us to show the
equivalence between Gibbs measures and KMS states (the quantum analogous to the
Gibbs measures).
