Inertial effects on the Brownian gyrator

TL;DR

This paper explores how inertia influences the behavior and energetics of the Brownian gyrator, revealing that inertia reduces nonequilibrium effects and affects rotational stability, with implications for stochastic energetics analysis.

Contribution

It explicitly incorporates mass into the analysis of the Brownian gyrator, demonstrating how inertia alters dynamics, rotation, and energetics compared to the overdamped case.

Findings

Inertia diminishes nonequilibrium effects and rotation in the Langevin model.

Rotation peaks at specific anisotropy, while stability minimizes at certain mass values.

The angular momentum $j_\theta$ effectively estimates stochastic energetics in the underdamped regime.

Abstract

The recent interest into the Brownian gyrator has been confined chiefly to the analysis of Brownian dynamics both in theory and experiment despite the applicability of general cases with definite mass. Considering mass explicitly in the solution of the Fokker--Planck equation and Langevin dynamics simulations, we investigate how inertia can change the dynamics and energetics of the Brownian gyrator. In the Langevin model, the inertia reduces the nonequilibrium effects by diminishing the declination of the probability density function and the mean of a specific angular momentum, $j_\theta$, as a measure of rotation. Another unique feature of the Langevin description is that rotation is maximized at a particular anisotropy while the stability of the rotation is minimized at a particular anisotropy or mass. Our results suggest that the Langevin dynamics description of the Brownian gyrator is intrinsically different from that with Brownian dynamics. In addition, $j_\theta$ is proven to be essential and convenient for estimating stochastic energetics such as heat currents and entropy production even in the underdamped regime.