Many-body problem

Quantum mechanics

Theoretical physics

Cell biology

Many-body theory

Biology

Materials science

Brownian motion

Density functional theory

Range (aeronautics)

Active matter

Variational principle

Classical mechanics

Statistical physics

Physics

Degrees of freedom (physics and chemistry)

Inertial frame of reference

Brownian dynamics

Composite material

Dynamical systems theory

Non-equilibrium thermodynamics

Reviews of Modern Physics

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.

Power functional theory for many-body dynamics