Entropy-production fluctuation theorem for a generalized Langevin particle in crossed electric and magnetic fields

TL;DR

This paper investigates the entropy production fluctuations of a charged Brownian particle in a harmonic trap under crossed electric and magnetic fields, using a generalized Langevin equation with memory to derive an exact fluctuation theorem.

Contribution

It provides an exact analytical derivation of the fluctuation theorem for entropy production in a non-Markovian Langevin system with external fields.

Findings

Entropy production obeys a detailed fluctuation theorem.

Exact solutions for Gaussian phase-space probability density.

Analytical results for specific driving protocols.

Abstract

We study fluctuations of entropy production for a charged Brownian particle confined in a harmonic trap and driven out of equilibrium by crossed electric and magnetic fields. The magnetic field is constant and perpendicular to the plane of motion, while the electric field is time dependent and provides the driving. The non-Markovian dynamics is modeled by a generalized Langevin equation with memory and Gaussian noise. Using the exact solution of this linear dynamics, we obtain the time-dependent Gaussian phase-space probability density and from it compute the trajectory-dependent total entropy production. For two solvable driving protocols, we prove analytically that the entropy production obeys a detailed fluctuation theorem.