  A path integral formalism for non-equilibrium systems is proposed based on a
manifold of quasi-equilibrium densities. A generalized Boltzmann principle is
used to weight manifold paths with the exponential of minus the information
discrepancy of a particular manifold path with respect to full Liouvillean
evolution. The likelihood of a manifold member at a particular time is termed a
consistency distribution and is analogous to a quantum wavefunction. The
Lagrangian here is of modified generalized Onsager-Machlup form. For large
times and long slow timescales the thermodynamics is of Oettinger form. The
proposed path integral has connections with those occuring in the quantum
theory of a particle in an external electromagnetic field. It is however
entirely of a Wiener form and so practical to compute. Finally it is shown that
providing certain reasonable conditions are met then there exists a unique
steady-state consistency distribution.
