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

TL;DR

This work addresses entropy-production fluctuations for a charged Brownian particle in a harmonic trap under a constant magnetic field and a time-dependent in-plane electric field, modeled by a non-Markovian generalized Langevin equation. By solving the linear GLE exactly, the authors obtain a time-dependent Gaussian phase-space distribution and show that the trajectory-dependent total entropy production is Gaussian with a variance equal to twice its mean, enabling a detailed fluctuation theorem. For two solvable driving protocols—a time-dependent force field and dragging the trap center—the study derives explicit expressions for the mean and variance of the work and entropy production, demonstrating that $P(\Delta s_{tot})/P(-\Delta s_{tot})=e^{\Delta s_{tot}}$ and $\langle e^{-\Delta s_{tot}}\rangle=1$ hold in this non-Markovian, magnetized setting. These results extend fluctuation-theorem theory to non-Markovian, magneto-electrostatic systems and provide a framework for experimental tests in viscoelastic or charged-particle contexts with magnetic fields.

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.