The aim of this work is to describe diffusion-like paths that are explored by a particle moving in a potential while being in thermal equilibrium with its surroundings. To do this, we examine functionals that are similar to the Onsager-Machlup functional. The difference is that they are based on Hamiltonian or Hybrid Monte Carlo methods (HMC) instead of Brownian dynamics. Then we focus our attention to the ``double-ended'' problem, where the Onsager-Machlup functional is interpreted as a ``thermodynamic action'' and is used to define a measure, which in turn can be employed to sample paths that are constrained to start and end at predetermined points. Even in simple systems, we find that the paths generated by sampling this measure are not consistent with the Boltzmann distribution. By using the new perspective described in the first part of the talk, I will identify why this is so. \ \ (co-work with Patrick Malsom)