Onsager-Machlup theory and work fluctuation theorem for a harmonically driven Brownian particle

TL;DR

This paper extends the Onsager-Machlup theory and work fluctuation theorem to a harmonically driven Brownian particle under oscillatory external forces, providing a comprehensive analysis of nonequilibrium steady and oscillatory states.

Contribution

It introduces a frequency-dependent work distribution function and proves a work fluctuation theorem valid at all times for a driven Brownian particle with time-dependent protocols.

Findings

Work fluctuation theorem holds for any initial distribution and at all times.

Derived frequency-dependent work distribution function using Onsager-Machlup Lagrangian.

Analyzed entropy production and dissipation functions in the system.

Abstract

We extend Tooru-Cohen analysis for nonequilirium steady state(NSS) of a Brownian particle to nonequilibrium oscillatory state (NOS) of Brownian particle by considering time dependent external drive protocol. We consider an unbounded charged Brownian particle in the presence of an oscillating electric field and prove work fluctuation theorem, which is valid for any initial distribution and at all times. For harmonically bounded and constantly dragged Brownian particle considered by Tooru and Cohen, work fluctuation theorem is valid for any initial condition(also NSS), but only in large time limit. We use Onsager-Machlup Lagrangian with a constraint to obtain frequency dependent work distribution function, and describe entropy production rate and properties of dissipation functions for the present system using Onsager-Machlup functional.