# Non-equilibrium driven by an external torque in the presence of a magnetic field

## TL;DR

This paper studies the non-equilibrium behavior of a colloid in a harmonic trap under an external torque and magnetic field, revealing conditions for steady state and analyzing non-equilibrium properties.

## Contribution

It derives conditions for steady state existence and explores the effects of non-conservative forces and magnetic fields on non-equilibrium characteristics.

## Key findings

- Steady state exists only within specific parameter ranges.
- Magnetic field influences probability distribution and currents.
- Violation of fluctuation-dissipation relation observed.

## Abstract

We investigate a motion of a colloid in a harmonic trap driven out of equilibrium by an external non-conservative force producing a torque in the presence of a uniform magnetic field. We find that steady state exists only for a proper range of parameters such as mass, viscosity coefficient, and stiffness of the harmonic potential, and the magnetic field, which is not observed in the overdamped limit. We derive the existence condition for the steady state. We examine the combined influence of the non-conservative force and the magnetic field on non-equilibrium characteristics such as non-Boltzmann steady-state probability distribution function, probability currents, entropy production, position-velocity correlation, and violation of fluctuation-dissipation relation.