Particle conservation in dynamical density functional theory.

Area of Science:

• Classical Fluid Dynamics
• Statistical Mechanics
• Computational Physics

Background:

• Dynamical density functional theory (dDFT) often exhibits erroneous particle number fluctuations.
• Understanding and accurately modeling the dynamics of inhomogeneous classical fluids is crucial for various scientific disciplines.
• Existing theories may struggle with systems exhibiting hard core interactions or non-equilibrium conditions.

Purpose of the Study:

• To present an exact adiabatic theory for the dynamics of inhomogeneous classical fluid density distributions.
• To resolve the issue of erroneous particle number fluctuations in dynamical density functional theory.
• To provide a robust theoretical framework applicable to both canonical and grand canonical systems.

Main Methods:

• Developed an exact adiabatic theory based on classical fluid dynamics.
• Derived a canonical free energy functional that governs adiabatic interparticle forces.
• Incorporated exact and advanced approximate hard core free energy functionals.

Main Results:

• The presented theory successfully eliminates erroneous particle number fluctuations.
• The derived canonical free energy functional accurately describes adiabatic interparticle forces for overdamped Brownian motion.
• Excellent agreement was achieved between theoretical predictions and simulation data, particularly with hard core potentials.

Conclusions:

• The exact adiabatic theory offers a significant advancement in modeling classical fluid dynamics.
• The theory provides a reliable method for simulating finite systems, both in and out of equilibrium.
• This work resolves key limitations of previous dynamical density functional theories.