  Onsager and Machlup proposed a second order variational-principle in order to
include inertial effects into the Langevin-equation, giving a Lagrangian with
second order derivatives in time. This but violates Ostrogradysky's theorem,
which proves that Lagrangians with higher than first order derivatives are
meaningless. As a consequence, inertial effects cannot be included in a
standard way. By using the canonical formalism, we suggest a solution to this
fundamental problem. Furthermore, we provide elementary arguments about the
hierarchy of immersions and actions between an ideal system and several
environments and show, that the structure of the Lagrangian sensitively depends
on this hierarchy.
