Fluctuation theorems and atypical trajectories

TL;DR

This paper analytically explores fluctuation theorems in simple models, examining the distribution of physical quantities along individual trajectories and identifying the behavior of atypical trajectories as observation time increases.

Contribution

It provides an analytical study of fluctuation theorems for various physical quantities and analyzes the behavior of atypical trajectories in nonlinear models.

Findings

Fraction of atypical trajectories decreases with observation time.

Distributions of thermodynamic work and entropy production can peak in the atypical regime.

Dissipated heat and classical work peak in the typical regime.

Abstract

In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities like the classical work ($W_c$), thermodynamic work ($W$), total entropy ($\Delta s_{tot}$) and dissipated heat ($Q$), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at macroscale. Nature of distributions for the thermodynamic work and the entropy production in nonlinear models may exhibit peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit peak in the regime of typical behaviour only.