Generalized Langevin and Nos{\'e}-Hoover processes absorbed at the boundary of a metastable domain

In this paper, we prove in a very weak regularity setting existence and uniqueness of quasi-stationary distributions as well as exponential convergence towards the quasi-stationary distribution for the generalized Langevin and the Nos{\'e}-Hoover processes, two processes which are widely used in molecular dynamics. The case of singular potentials is considered. With the techniques used in this work, we are also able to greatly improve existing results on quasi-stationary distributions for the kinetic Langevin process to a weak regularity setting.