Velocity gradient power functional for Brownian dynamics

TL;DR

This paper introduces a new approximation for the superadiabatic free power functional in Brownian dynamics, which depends on local velocity gradients and captures viscous forces beyond traditional density functional theory, validated by simulations.

Contribution

It provides a novel, explicit approximation for superadiabatic forces in overdamped Brownian systems based on velocity gradients, extending current theoretical frameworks.

Findings

High accuracy in predicting superadiabatic forces

Captures viscous effects beyond dynamical density functional theory

Validated through comparison with simulation results

Abstract

We present an explicit and simple approximation for the superadiabatic excess (over ideal gas) free power functional, admitting the study of the nonequilibrium dynamics of overdamped Brownian many-body systems. The functional depends on the local velocity gradient and is systematically obtained from treating the microscopic stress distribution as a conjugate field. The resulting superadiabatic forces are beyond dynamical density functional theory and are of viscous nature. Their high accuracy is demonstrated by comparison to simulation results.