Power functional theory for Brownian dynamics.

Area of Science:

• Statistical Mechanics
• Computational Physics
• Chemical Physics

Background:

• Classical density functional theory (DFT) is an exact variational method for equilibrium properties of fluids.
• Studying non-equilibrium dynamics of classical many-body systems is computationally challenging.

Purpose of the Study:

• To generalize classical DFT for non-equilibrium dynamics.
• To develop a theoretical framework for systems far from equilibrium.

Main Methods:

• A dynamical functional based on reversible free energy and irreversible power dissipation was formulated.
• Minimization of the
• free power
• functional with respect to the one-body current yields equations of motion.
• Approximations to power dissipation allow for tractable calculations.

Main Results:

• The theory recovers equilibrium DFT in the equilibrium limit.
• Adiabatic dynamical density functional theory emerges from an ideal gas approximation.
• Approximations to excess power dissipation enable studies beyond the adiabatic regime.

Conclusions:

• The generalized DFT provides a versatile framework for non-equilibrium statistical mechanics.
• This approach facilitates the systematic study of complex dynamics in classical many-body systems.
• The method opens new avenues for simulating systems far from equilibrium.