Power functional theory for active Brownian particles: General formulation and power sum rules.

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Active Matter

Background:

• Generalizing power functional theory (PFT) to systems with orientational degrees of freedom.
• Enabling the study of active particles in complex, time-dependent, and inhomogeneous nonequilibrium conditions.

Purpose of the Study:

• To extend PFT to Brownian many-body systems with orientational degrees of freedom.
• To develop a variational framework for analyzing active particle dynamics in nonequilibrium steady states.

Main Methods:

• Generalization of power functional theory to include orientational degrees of freedom.
• Derivation of relationships between free power, dissipated work, and particle dynamics.
• Brownian dynamics simulations of active Brownian spheres to validate the theory.

Main Results:

• Proved that free power equals half the negative dissipated external work per time in steady states.
• Developed a variational theory expressing free power as a functional of density and current distributions.
• Approximated superadiabatic contributions to excess dissipation due to drag.

Conclusions:

• The generalized PFT framework successfully describes active particle systems.
• The theory provides a good account of simulation data for soft repulsive spheres.
• The approach offers a pathway to understanding nonequilibrium phenomena in active matter.