Classical and Thermodynamic work fluctuations

TL;DR

This paper investigates classical and thermodynamic work fluctuations in non-equilibrium systems, analyzing their behavior over time and discussing the applicability of fluctuation theorems in linear and nonlinear models.

Contribution

It provides analytical expressions for fluctuation trajectories and explores the relationship between different types of work and heat fluctuations in non-equilibrium states.

Findings

Number of atypical trajectories decreases with observation time.

Trajectories with negative classical work may not correspond to negative thermodynamic work or heat.

Steady state fluctuation theorems are applicable in both linear and nonlinear models.

Abstract

We have studied the nature of classical work ($W_{c}$) and thermodynamic work ($W$) fluctuations in systems driven out of equilibrium both in transient and time periodic steady state. As the observation time of trajectory increases, we show that the number of trajectories which exhibit excursions away from the typical behaviour i.e., $W_{c}<0$, $W<\Delta F$ and dissipated heat $Q<0$ decreases as anticipated for macroscopic time scales. Analytical expressions for such trajectories are obtained. Trajectory for which $W_{c}<0$ may not correspond to $W<\Delta F$ or $Q<0$. The applicability of steady state fluctuation theorems are discussed in our linear as well as nonlinear models.