Path ensembles averages in systems driven far-from-equilibrium

TL;DR

This paper unifies several key nonequilibrium relations into a single theorem for Markovian systems, providing a broader understanding of systems driven far from equilibrium.

Contribution

It derives a unified theorem encompassing the Kawasaki relation, fluctuation theorem, and Jarzynski relation for discrete Markovian dynamics.

Findings

Unified theorem for nonequilibrium relations

Applicable to discrete time and space Markov processes

Conditions include preservation of equilibrium and finite energy

Abstract

The Kawasaki nonlinear response relation, the transient fluctuation theorem, and the Jarzynski nonequilibrium work relation are all expressions that describe the behavior of a system that has been driven from equilibrium by an external perturbation. In contrast to linear response theory, these expressions are exact no matter the strength of the perturbation, or how far the system has been driven away from equilibrium. In this paper I show that these three relations (and several other closely related results) can all be considered special cases of a single theorem. This expression is explicitly derived for discrete time and space Markovian dynamics, with the additional assumptions that the single time step dynamics preserve the appropriate equilibrium ensemble, and that the energy of the system remains finite.