Brownian Motions in Two Dimensions under Non-harmonic Potentials: Nonequilibrium Steady-State Dynamics

A Brownian gyrator features a two-dimensional random particle under a harmonic potential, while random thermal kicks are of distinct temperatures along the two axes [Filliger and Reimann, Phys. Rev. Lett. 99, 230602 (2007)]. In our current work, we replace the harmonic potential by other types of potentials, and we investigate the nonequilibrium steady states (NESS) through simulation studies. In contrast to the Brownian-gyrator case, where the average flux circulates along the probability contour, our results for the non-harmonic cases do not follow this signature. Moreover, the violation of this feature exists even near the potential energy minima, where the harmonic approximation work. For the special case with a symmetric quartic potential, we provide a simple argument for this less intuitive behavior.