Entropy Production in Collisionless Systems. III. Results from Simulations

TL;DR

This paper investigates the equilibria of collisionless self-gravitating systems formed in N-body simulations, demonstrating that some initial conditions lead to states well-described by maximum entropy models, with entropy calculations confirming this.

Contribution

It provides evidence that certain collisionless systems reach maximum entropy states, validating thermodynamically-motivated models against simulation results.

Findings

Equilibria can be accurately modeled by maximum entropy distribution functions.

Simulations show systems reaching maximum entropy states.

Results are consistent across various initial conditions and numerical setups.

Abstract

The equilibria formed by the self-gravitating, collisionless collapse of simple initial conditions have been investigated for decades. We present the results of our attempts to describe the equilibria formed in $N$-body simulations using thermodynamically-motivated models. Previous work has suggested that it is possible to define distribution functions for such systems that describe maximum entropy states. These distribution functions are used to create radial density and velocity distributions for comparison to those from simulations. A wide variety of $N$-body code conditions are used to reduce the chance that results are biased by numerical issues. We find that a subset of initial conditions studied lead to equilibria that can be accurately described by these models, and that direct calculation of the entropy shows maximum values being achieved.