A Path Integral Formalism for Nonequilibrium Hamiltonian Statistical Systems
Abstract
A path integral formalism for nonequilibrium systems is proposed based on a manifold of quasiequilibrium 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 OnsagerMachlup 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 steadystate consistency distribution.
 Publication:

Journal of Statistical Physics
 Pub Date:
 March 2015
 DOI:
 10.1007/s109550141149x
 arXiv:
 arXiv:1307.1102
 Bibcode:
 2015JSP...158.1271K
 Keywords:

 Nonequilibrium;
 Path Integral;
 Closure;
 Mathematical Physics
 EPrint:
 28 pages 4 figures