A Path Integral Formalism for Non-equilibrium Hamiltonian Statistical Systems

Richard Kleeman

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)1271-1297
Number of pages27
JournalJournal of Statistical Physics
Issue number6
StatePublished - Mar 2015


  • Closure
  • Non-equilibrium
  • Path Integral

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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