Work fluctuations for Bose particles in grand canonical initial states

TL;DR

This paper studies work fluctuations in Bose particles within a harmonic trap, analyzing how initial conditions affect the divergence of work-related statistical measures and characterizing the work distribution's shape at different temperatures.

Contribution

It provides a detailed analysis of the work distribution and divergence conditions for Bose particles in a harmonic trap under various reservoir conditions.

Findings

At low temperatures, the work PDF is highly asymmetric with exponential tails.

At high temperatures, the work PDF approaches a Gaussian distribution.

Divergence of the exponentiated work average depends on trap width and temperature.

Abstract

We consider bosons in a harmonic trap and investigate the fluctuations of the work performed by an adiabatic change of the trap curvature. Depending on the reservoir conditions such as temperature and chemical potential that provide the initial equilibrium state, the exponentiated work average (EWA) defined in the context of the Crooks relation and the Jarzynski equality may diverge if the trap becomes wider. We investigate how the probability distribution function (PDF) of the work signals this divergence. It is shown that at low temperatures the PDF is highly asymmetric with a steep fall off at one side and an exponential tail at the other side. For high temperatures it is closer to a symmetric distribution approaching a Gaussian form. These properties of the work PDF are discussed in relation to the convergence of the EWA and to the existence of the hypothetical equilibrium state to which those thermodynamic potential changes refer that enter both the Crooks relation and the Jarzynski equality.