## 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 Öttinger 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.

Original language | English (US) |
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Pages (from-to) | 1271-1297 |

Number of pages | 27 |

Journal | Journal of Statistical Physics |

Volume | 158 |

Issue number | 6 |

DOIs | |

State | Published - Mar 2015 |

## Keywords

- Closure
- Non-equilibrium
- Path Integral

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics