L${}^2$-Hypocoercivity for non-equilibrium kinetic equations

The recent work [11] developed a general framework to show hypocoercivity for a stationary Gibbs state and allowed spatial degeneracy, confining potentials and boundary conditions. In this work, we show that the explicit energy approach in the weighted L${}^2$ space works for general non-equilibrium steady states and that it can be adapted to cases with weaker confinement leading to algebraic decay.