Nonequilibrium steady state of a stochastic system driven by a nonlinear drift force

Area of Science:

• Statistical Physics
• Nonlinear Dynamics
• Stochastic Processes

Background:

• Investigating nonequilibrium steady states (NESS) is crucial for understanding complex systems.
• Previous work established NESS current circulation on equiprobability surfaces for linear drift forces.

Purpose of the Study:

• To analyze the properties of NESS in stochastic systems driven by nonlinear drift forces.
• To understand how non-identically and independently distributed noises affect NESS.
• To characterize the behavior of NESS current and probability distributions under nonlinear driving.

Main Methods:

• Perturbation theory applied to cubic and quartic coefficients of the nonlinear drift force.
• Analysis of stochastic systems with non-identically and independently distributed noises.
• Comparison of theoretical predictions with computer simulations.

Main Results:

• The probability maximum shifts from the fixed point of the drift force in nonlinear systems.
• The NESS current exhibits nontrivial circulation, deviating from equiprobability surfaces.
• Multiple centers of the NESS current are observed, not coinciding with the probability maximum.

Conclusions:

• Nonlinear drift forces lead to complex potential landscapes and NESS current behavior.
• The findings extend the understanding of NESS beyond linear systems.
• Theoretical predictions are validated by computational evidence.