Power functional theory for many-body dynamics

TL;DR

Power functional theory offers a comprehensive variational framework for describing the complex dynamics of many-body systems, unifying equilibrium and nonequilibrium phenomena through one-body correlation functions.

Contribution

This work introduces a novel power functional approach that extends density functional theory to dynamic many-body systems, enabling accurate descriptions of diverse nonequilibrium processes.

Findings

Successfully describes van Hove functions in liquids

Models flow in nonequilibrium steady states

Analyzes motility-induced phase separation and shear phenomena

Abstract

The rich and diverse dynamics of particle-based systems ultimately originates from the coupling of their degrees of freedom via internal interactions. To arrive at a tractable approximation of such many-body problems, coarse-graining is often an essential step. Power functional theory provides a unique and microscopically sharp formulation of this concept. The approach is based on an exact one-body variational principle to describe the dynamics of both overdamped and inertial classical and quantum many-body systems. In equilibrium, density functional theory is recovered, and hence spatially inhomogeneous systems are described correctly. The dynamical theory operates on the level of time-dependent one-body correlation functions. Two- and higher-body correlation functions are accessible via the dynamical test particle limit and the nonequilibrium Ornstein-Zernike route. We describe the structure of this functional approach to many-body dynamics, including much background as well as applications to a broad range of dynamical situations, such as the van Hove function in liquids, flow in nonequilibrium steady states, motility-induced phase separation of active Brownian particles, lane formation in binary colloidal mixtures, and both steady and transient shear phenomena.