Nonequilibrium Ornstein-Zernike relation for Brownian many-body dynamics

TL;DR

This paper develops a dynamic Ornstein-Zernike equation for nonequilibrium Brownian fluids, linking two-time correlations with one-body fields through a unified functional framework.

Contribution

It introduces a non-Markovian, functional calculus-based approach that unifies mode-coupling theory and dynamical density functional theory for driven Brownian systems.

Findings

Derivation of a nonequilibrium Ornstein-Zernike relation.

Identification of memory functions as functional derivatives.

Proposal of an excess dissipation functional unifying existing theories.

Abstract

We derive a dynamic Ornstein-Zernike equation for classical fluids undergoing overdamped Brownian motion and driven out of equilibrium. Inhomogeneous two-time correlation functions are obtained from functional differentiation of the one-body density and current with respect to an appropriately chosen external field. Functional calculus leads naturally to non-Markovian equations of motion for the two-time correlators. Memory functions are identified as functional derivatives of a space- and time-nonlocal power dissipation functional. We propose an excess (over ideal gas) dissipation functional that both generates mode-coupling theory for the two-body correlations and extends dynamical density functional theory for the one-body fields, thus unifying the two approaches.