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
        }
}
  • M. Schmidt
  • Published 23 January 2018
  • Physics, Mathematics
  • The Journal of chemical physics
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… 

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References

SHOWING 1-10 OF 45 REFERENCES

Power functional theory for Brownian dynamics.

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.

  • M. Schmidt
  • Physics
    The 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.

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

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.

  • A. Archer
  • Physics
    The 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.

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.

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.

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.

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.

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.