Correlations in multithermostat Brownian systems with Lorentz force

TL;DR

This paper investigates how Lorentz force induces correlations and non-Boltzmann steady states in multithermostat Brownian systems, revealing spatially correlated diffusion and flux-free non-equilibrium distributions.

Contribution

It introduces a novel analysis of Lorentz-force-induced correlations in multithermostat Brownian particles, showing non-Boltzmann steady states and spatially correlated diffusion.

Findings

Lorentz force causes velocity component correlations.

Diffusion matrix eigenvectors do not align with temperature axes.

Non-Boltzmann steady states can be rotated by reversing magnetic field.

Abstract

We study the motion of a Brownian particle subjected to Lorentz force due to an external magnetic field. Each spatial degree of freedom of the particle is coupled to a different thermostat. We show that the magnetic field results in correlation between different velocity components in the stationary state. Integrating the velocity autocorrelation matrix, we obtain the diffusion matrix that enters the Fokker-Planck equation for the probability density. The eigenvectors of the diffusion matrix do not align with the temperature axes. As a consequence the Brownian particle performs spatially correlated diffusion. We further show that in the presence of an isotropic confining potential, an unusual, flux-free steady state emerges which is characterized by a non-Boltzmann density distribution, which can be rotated by reversing the magnetic field. The nontrivial steady state properties of our system result from the Lorentz force induced coupling of the spatial degrees of freedom which cease to exist in equilibrium corresponding to a single-temperature system.