Autonomous Brownian gyrators: a study on gyrating characteristics

TL;DR

This study investigates the nonequilibrium steady-state dynamics of two-dimensional Brownian gyrators with harmonic and nonharmonic potentials, revealing distinct gyrating patterns and critical behaviors through simulations and Fokker-Planck analysis.

Contribution

It introduces two simple methods to understand gyrating patterns and compares the dynamics of harmonic and nonharmonic potentials in Brownian gyrators.

Findings

Harmonic potentials show gyrating currents along equiprobability contours.

Nonharmonic potentials exhibit distinct gyrating patterns from probability distributions.

Critical double-well potential case shows absence of harmonic contribution to gyration.

Abstract

We study the nonequilibrium steady-state (NESS) dynamics of two-dimensional Brownian gyrators under harmonic and nonharmonic potentials via computer simulations and analyses based on the Fokker-Planck equation, while our nonharmonic cases feature a double-well potential and an isotropic quartic potential. In particular, we report two simple methods that can help understand gyrating patterns. For harmonic potentials, we use the Fokker-Planck equation to survey the NESS dynamical characteristics, i.e., the NESS currents gyrate along the equiprobability contours and the stationary point of flow coincides with the potential minimum. As a contrast, the NESS results in our nonharmonic potentials show that these properties are largely absent, as the gyrating patterns are much distinct from those of corresponding probability distributions. Furthermore, we observe a critical case of the double-well potential, where the harmonic contribution to the gyrating pattern becomes absent, and the NESS currents do not circulate about the equiprobability contours nearby the potential minima even at low temperatures.