  We propose three new discrete variational schemes that capture the
conservative-dissipative structure of a generalized Kramers equation. The first
two schemes are single-step minimization schemes while the third one combines a
streaming and a minimization step. The cost functionals in the schemes are
inspired by the rate functional in the Freidlin-Wentzell theory of large
deviations for the underlying stochastic system. We prove that all three
schemes converge to the solution of the generalized Kramers equation.
