Onsager-Machlup theory for nonequilibrium steady states and fluctuation theorems

TL;DR

This paper extends the Onsager-Machlup theory to nonequilibrium steady states, deriving fluctuation theorems for work and heat using a functional integral approach for a dragged particle in a heat reservoir.

Contribution

It introduces a generalized Onsager-Machlup framework for nonequilibrium steady states and establishes new fluctuation theorems related to work and heat.

Findings

Derived fluctuation theorem for work in nonequilibrium steady states.

Extended fluctuation theorem for heat in long time limit.

Established nonequilibrium detailed balance relations.

Abstract

A generalization of the Onsager-Machlup theory from equilibrium to nonequilibrium steady states and its connection with recent fluctuation theorems are discussed for a dragged particle restricted by a harmonic potential in a heat reservoir. Using a functional integral approach, the probability functional for a path is expressed in terms of a Lagrangian function from which an entropy production rate and dissipation functions are introduced, and nonequilibrium thermodynamic relations like the energy conservation law and the second law of thermodynamics are derived. Using this Lagrangian function we establish two nonequilibrium detailed balance relations, which not only lead to a fluctuation theorem for work but also to one related to energy loss by friction. In addition, we carried out the functional integrals for heat explicitly, leading to the extended fluctuation theorem for heat. We also present a simple argument for this extended fluctuation theorem in the long time limit.