A Monte Carlo Method for Calculating Lynden-Bell Equilibrium in Self-Gravitating Systems

Area of Science:

• Astrophysical plasmas
• Statistical mechanics
• Computational physics

Background:

• Lynden-Bell (LB) entropy maximization is crucial for understanding violent relaxation in collisionless systems.
• Direct maximization is computationally intensive, limited to simple initial conditions.
• Previous studies were restricted due to the complexity of handling Casimir invariants.

Purpose of the Study:

• To develop an accessible Monte Carlo method for Lynden-Bell entropy maximization.
• To investigate LB entropy maximization for arbitrary initial particle distributions.
• To compare simulation results with Lynden-Bell's violent relaxation theory.

Main Methods:

• Discretization of arbitrary initial particle distributions into density levels.
• Evolution of density levels using an efficient Monte Carlo algorithm.
• Comparison of equilibrium states with explicit Molecular Dynamics simulations.

Main Results:

• The Monte Carlo approach facilitates LB entropy maximization for diverse initial conditions.
• Incomplete relaxation was observed in most tested initial distributions.
• Stationary particle distributions exhibited hard cutoffs, differing from LB's predicted algebraic decay.

Conclusions:

• The developed Monte Carlo method offers a practical tool for studying LB entropy maximization.
• Violent relaxation may not always lead to the predicted Lynden-Bell equilibrium state.
• The study highlights discrepancies between theoretical predictions and simulation outcomes for particle distribution tails.