Statistical Mechanics of Unbound Two Dimensional Self-Gravitating Systems

TL;DR

This paper investigates the relaxation dynamics of two-dimensional self-gravitating systems, revealing how they approach equilibrium or become trapped in non-ergodic states, supported by theory and molecular dynamics simulations.

Contribution

It provides a new analytical theory describing the final stationary state of such systems without adjustable parameters.

Findings

Systems relax to Maxwell-Boltzmann distribution over time.

Relaxation time scales with the number of particles.

In the thermodynamic limit, systems do not reach equilibrium and become non-ergodic.

Abstract

We study, using both theory and molecular dynamics simulations, the relaxation dynamics of a microcanonical two dimensional self-gravitating system. After a sufficiently large time, a gravitational cluster of N particles relaxes to the Maxwell-Boltzmann distribution. The time to reach the thermodynamic equilibrium, however, scales with the number of particles. In the thermodynamic limit, $N\to\infty$ at fixed total mass, equilibrium state is never reached and the system becomes trapped in a non-ergodic stationary state. An analytical theory is presented which allows us to quantitatively described this final stationary state, without any adjustable parameters.