The notion of canonical energy in general relativity provides a link between dynamical and thermodynamical notions of stability and instability of stationary spacetimes (at the linearized level). In this talk, I review this link and present some applications. One is a general argument that any asymptotically AdS-spacetime with an ergo-region must be unstable (super-radiant instability). Another application are stability results for higher dimensional black holes under perturbations that are invariant under an isometric action of a torus ("axi-symmetric"), thereby providing also relationship with mass-angular momentum inequalities of Dain et al.