Power functional theory for Newtonian many-body dynamics

Area of Science:

• Classical mechanics
• Non-equilibrium statistical physics
• Theoretical physics

Background:

• Understanding the dynamics of classical many-body systems far from equilibrium is crucial.
• Existing theories often struggle to capture inertial effects in these systems.

Purpose of the Study:

• To construct a variational theory for the inertial dynamics of classical many-body systems out of equilibrium.
• To provide a unique determination of system time evolution.

Main Methods:

• Development of a variational theory based on a power rate functional.
• The functional depends on time- and space-dependent one-body distributions (density, particle current, time derivative of current).
• Utilizing Euler-Lagrange equations and the continuity equation.

Main Results:

• The governing functional is minimized by the true time derivative of the current.
• The Euler-Lagrange equation, coupled with the continuity equation, uniquely determines system time evolution.
• An adiabatic approximation introduces free energy and Brownian power functionals for systems like liquids at constant temperature.

Conclusions:

• The developed variational theory offers a novel approach to describing non-equilibrium inertial dynamics.
• The theory provides a framework for understanding forces beyond the overdamped Brownian limit.
• This work lays the foundation for further investigations into complex system dynamics.