Nonequilibrium Work distributions for a trapped Brownian particle in a time dependent magnetic field

TL;DR

This paper investigates the work distributions of a charged Brownian particle in a time-dependent magnetic field, demonstrating the magnetic field's irrelevance to free energy and identifying parametric resonance phenomena.

Contribution

It introduces a novel approach to calculating work involving vector potential variation and confirms the magnetic field's non-effect on free energy, extending thermodynamic understanding.

Findings

Work distributions depend on the magnetic field protocol.

Free energy remains unaffected by magnetic field variations.

System exhibits parametric resonance under certain conditions.

Abstract

We study the dynamics of a trapped, charged Brownian particle in presence of a time dependent magnetic field. We calculate work distributions for different time dependent protocols. In our problem thermodynamic work is related to variation of vector potential with time as opposed to the earlier studies where the work is related to time variation of the potentials which depends only on the coordinates of the particle. Using Jarzynski identity and Crook's equality we show that the free energy of the particle is independent of the magnetic field, thus complementing the Bohr-van Leeuwen theorem. We also show that our system exhibits a parametric resonance in certain parameter space.