Gravitation in the Microcanonical Ensemble: Appropriate Scaling Leading to Extensivity and Thermalization

TL;DR

This paper presents a model of gravitationally interacting hard spheres, demonstrating that appropriate scaling preserves extensivity and leads to spontaneous local thermalization, with density profiles derived via hydrostatic equilibrium.

Contribution

It introduces a scaling limit for gravitational systems that maintains extensivity and reveals spontaneous local thermalization within a microcanonical framework.

Findings

Extensivity preserved despite long-range gravity

Spontaneous local thermalization observed

Density profiles derived from hydrostatic equilibrium

Abstract

We introduce a simple model of hard spheres with gravitational interactions, for which we study a suitable scaling limit. Usual extensive properties are maintained notwithstanding the long range of gravitational interaction. We show that a local thermalization spontaneously emerges within a microcanonical description of the stationary state. In the considered scaling limit, the resulting density profile can be determined in a hydrostatic approach.