System-Bath Approach to Rotating Brownian Motion

TL;DR

This paper investigates the dynamics of a Brownian particle in a rotating thermal bath, revealing how rotation affects equilibrium states, noise correlations, and work extraction, with implications for classical statistical mechanics.

Contribution

It introduces a first-principles analysis of rotating Brownian systems, showing the impact of rotation on equilibrium distributions, noise correlations, and work extraction possibilities.

Findings

Rotating systems exhibit long-range correlated noise in the Langevin equation.

Weak coupling recovers the rotating Gibbs distribution; strong coupling does not.

Work can be extracted from asymmetric potentials under rotation.

Abstract

Rotating equilibrated systems are widespread, but relatively little attention has been devoted to studying them from the first principles of statistical mechanics. We fill this gap by studying a Brownian particle coupled with a thermal bath made of rotating harmonic oscillators. We show that the Langevin equation that describes the dynamics of the Brownian particle contains (due to rotation) long-range correlated noise. In contrast to the usual situation of (non-rotating) equilibration, the rotating Gibbs distribution is recovered only for a weak coupling with the bath. In the presence of a uniform magnetic field, the stationary state is not Gibbsian, even under weak coupling. In this context, we clarify the applicability of the Bohr-van Leeuwen theorem to classical systems in rotating equilibrium, as well as the concept of work done by a changing magnetic field. We show that the Brownian particle under a rotationally symmetric potential reaches a stationary state that behaves as an effective equilibrium, characterized by a free energy. As a result, no work can be extracted via cyclic processes that respect the rotation symmetry. However, if the external potential exhibits asymmetry, then work extraction via slow cyclic processes is possible. This is illustrated by a general scenario involving a slow rotation of a non-rotation-symmetric potential. We study sedimentation equilibrium and show that centrifugal instability is prevented by a finite friction.