Nonequilibrium Steady State Driven by a Nonlinear Drift Force

TL;DR

This paper explores the properties of nonequilibrium steady states in stochastic systems with nonlinear drift forces and non-uniform noises, revealing complex circulation patterns and shifts in probability maxima.

Contribution

It introduces a perturbation theory approach for nonlinear drift forces and uncovers new circulation behaviors and probability landscape shifts in NESS.

Findings

NESS current circulates off the equiprobability surface

Probability maximum shifts from the fixed point

Nontrivial circulation centers are identified

Abstract

We investigate the properties of the nonequilibrium steady state for the stochastic system driven by a nonlinear drift force and influenced by noises which are not identically and independently distributed. The nonequilibrium steady state (NESS) current results from a residual part of the drift force which is not cancelled by the diffusive action of noises. From our previous study for the linear drift force the NESS current was found to circulate on the equiprobability surface with the maximum at a stable fixed point of the drift force. For the nonlinear drift force, we use the perturbation theory with respect to the cubic and quartic coefficients of the drift force. We find an interesting potential landscape picture where the probability maximum shifts from the fixed point of the drift force and, furthermore, the NESS current has a nontrivial circulation which flows off the equiprobability surface and has various centers not located at the probability maximum. The theoretical result is well confirmed by the computer simulation.