A path integral formalism for non-equilibrium Hamiltonian statistical systems

Abstract

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.

28 pages 4 figures

References in corpus (3)

• The Kolmogorov-Riesz compactness theorem
• Onsager-Machlup theory for nonequilibrium steady states and fluctuation theorems
• An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics

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