# Power functional theory for Newtonian many-body dynamics.

@article{Schmidt2018PowerFT, title={Power functional theory for Newtonian many-body dynamics.}, author={Matthias Schmidt}, journal={The Journal of chemical physics}, year={2018}, volume={148 4}, pages={ 044502 } }

We construct a variational theory for the inertial dynamics of classical many-body systems out of equilibrium. The governing (power rate) functional depends on three time- and space-dependent one-body distributions, namely, the density, the particle current, and the time derivative of the particle current. The functional is minimized by the true time derivative of the current. Together with the continuity equation, the corresponding Euler-Lagrange equation uniquely determines the time evolution…

## 19 Citations

### Power functional theory for many-body dynamics

- PhysicsReviews of Modern Physics
- 2022

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…

### Force balance in thermal quantum many-body systems from Noether’s theorem

- Mathematics, PhysicsJournal of Physics A: Mathematical and Theoretical
- 2022

We address the consequences of invariance properties of the free energy of spatially inhomogeneous quantum many-body systems. We consider a specific position-dependent transformation of the system…

### Hydrodynamic density functional theory for mixtures from a variational principle and its application to droplet coalescence.

- PhysicsThe Journal of chemical physics
- 2021

This work identifies a suitable expression for driving forces for molecular diffusion of inhomogeneous systems and shows that the hydrodynamic DFT model, although not formulated in conservative form, globally satisfies the first and second law of thermodynamics.

### Noether’s theorem in statistical mechanics

- PhysicsCommunications Physics
- 2021

Noether’s calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather…

### Structural Nonequilibrium Forces in Driven Colloidal Systems.

- PhysicsPhysical review letters
- 2018

From the time evolution in the exact (Smoluchowski) low-density limit, Brownian dynamics simulations, and a novel power functional approximation, a quantitative understanding of viscous and structural forces, including memory and shear migration is obtained.

### Shear and Bulk Acceleration Viscosities in Simple Fluids.

- Biology, PhysicsPhysical review letters
- 2022

Using molecular and overdamped Brownian dynamics many-body simulations, it is demonstrated that analogous viscous effects act on the acceleration field, and this acceleration viscous behavior can be quantitatively described using simple exponentially decaying memory kernels.

### Superadiabatic Forces via the Acceleration Gradient in Quantum Many-Body Dynamics

- PhysicsMolecules
- 2019

It is shown that gradients of both the microscopic velocity and acceleration field are required to correctly describe the effects due to interparticle interactions and it is validated that superadiabatic contributions beyond the adiabatic approximation include effective dissipation.

### Classical dynamical density functional theory: from fundamentals to applications

- PhysicsAdvances in Physics
- 2020

Classical dynamical density functional theory (DDFT) is one of the cornerstones of modern statistical mechanics. It is an extension of the highly successful method of classical density functional…

### Deriving phase field crystal theory from dynamical density functional theory: Consequences of the approximations.

- PhysicsPhysical review. E
- 2019

Although PFC models are very successful as phenomenological models of crystallization, it is found impossible to derive the PFC as a theory for the (scaled) density distribution when starting from an accurate DDFT, without introducing spurious artifacts.

### Well-Posedness and Equilibrium Behaviour of Overdamped Dynamic Density Functional Theory

- Mathematics
- 2020

We establish the global well-posedness of overdamped dynamical density functional theory (DDFT): a nonlinear, nonlocal integro-partial differential equation used in statistical mechanical models of…

## References

SHOWING 1-10 OF 45 REFERENCES

### Power functional theory for Brownian dynamics.

- PhysicsThe Journal of chemical physics
- 2013

A generalization of DFT is reported to treat the non-equilibrium dynamics of classical many-body systems subject to Brownian dynamics, based upon a dynamical functional consisting of reversible free energy changes and irreversible power dissipation.

### Quantum power functional theory for many-body dynamics.

- PhysicsThe Journal of chemical physics
- 2015

A one-body variational theory for the time evolution of nonrelativistic quantum many-body systems where space- and time-nonlocal one- body forces are generated by the superadiabatic contribution to the functional.

### Velocity Gradient Power Functional for Brownian Dynamics.

- PhysicsPhysical review letters
- 2018

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…

### Beyond dynamic density functional theory: the role of inertia

- Physics
- 2008

We discuss the recent attempts to generalize dynamical density functional (DDF) theory to situations where the momentum and energy transport, not necessarily associated with mass diffusion, play a…

### Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics.

- PhysicsThe Journal of chemical physics
- 2009

The theory is extended and it is shown that the theory may be used to obtain the mode coupling theory that is widely used for describing the transition from a liquid to a glassy state.

### Dynamic correlations in Brownian many-body systems.

- MathematicsThe Journal of chemical physics
- 2014

For classical Brownian systems driven out of equilibrium, inhomogeneous two-time correlation functions are derived from functional differentiation of the one-body density and current with respect to external fields and memory functions are identified as functional derivatives of a unique space- and time-nonlocal dissipation power functional.

### Nonequilibrium Ornstein-Zernike relation for Brownian many-body dynamics.

- Physics, MathematicsThe Journal of chemical physics
- 2013

This work derives a dynamic Ornstein-Zernike equation for classical fluids undergoing overdamped Brownian motion and driven out of equilibrium and proposes an excess (over ideal gas) dissipation functional that both generates mode-coupling theory for the two-body correlations and extends dynamical density functional theory forThe one-body fields, thus unifying the two approaches.

### Superadiabatic forces in Brownian many-body dynamics.

- PhysicsPhysical review letters
- 2014

A simulation method is presented that allows us to isolate and precisely evaluate superadiabatic correlations and the resulting forces in classical Brownian many-body dynamics and provides a rational basis for the development of improved theories.

### Nonequilibrium inertial dynamics of colloidal systems.

- PhysicsThe Journal of chemical physics
- 2006

This work considers the properties of a one-dimensional fluid of Brownian inertial hard-core particles, whose microscopic dynamics is partially damped by a heat bath, and derives the evolution equation for the average density by means of a time multiple time-scale method.

### Phase-space approach to dynamical density functional theory.

- PhysicsThe Journal of chemical physics
- 2007

This study extends to arbitrary dimensions previous work on a one-dimensional fluid and highlights the subtleties of kinetic theory in the derivation of dynamical density functional theory.