Entropy production of a Brownian ellipsoid in the overdamped limit

TL;DR

This paper investigates the entropy production of an ellipsoidal Brownian particle in the overdamped limit, revealing additional anomalous contributions due to rotational motion, shape, and environmental heterogeneity, advancing stochastic thermodynamics understanding.

Contribution

It identifies and quantifies the additional anomalous entropy production from rotational motion in the overdamped limit of Brownian ellipsoids, extending previous theories.

Findings

Rotational motion adds to anomalous entropy production.

Explicit formulas derived for spheroids and near-spherical particles.

Overdamped equations of motion obtained with singular perturbation analysis.

Abstract

We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here, we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.