Exact distribution for work and stochastic efficiency of an isothermal machine

TL;DR

This paper derives the exact distribution of work and stochastic efficiency for an isothermal Brownian machine, validating fluctuation theorems and providing detailed probabilistic insights through analytical and numerical methods.

Contribution

It provides the first exact distribution of work and efficiency for a coupled Brownian particle system under isothermal conditions, including fluctuation theorem validation.

Findings

Transient fluctuation theorem holds for individual and total work.

Exact probability density functions for work and efficiency are derived.

Numerical simulations confirm analytical results.

Abstract

We consider an isothermal machine composed of two Brownian particles (say particle A and B) connected by a harmonic spring. A constant load is attached to particle A, and the particle B is trapped in a harmonic confinement whose minimum is dragged with a constant velocity. Whole system is in contact with the heat bath of a constant temperature. We obtain the distribution of the work done on particle A and particle B, and transient fluctuation theorem for these quantities is tested in the weak coupling limit and for both small and large observation time. Moreover, we show that the transient fluctuation theorem for total work done on both particles is satisfied. Furthermore, we compute the stochastic efficiency which is the ratio of the work done against the load force on particle A and the work done on particle B of this machine. The probability density function for stochastic efficiency is computed for all time. Numerical simulations are also done to verify the analytical results.