Inhomogeneous distribution particles in self-gravitational system

TL;DR

This paper derives the microcanonical partition function for a 3D self-gravitational system, revealing that inhomogeneous particle distributions with clustering increase entropy, indicating a tendency toward dispersion.

Contribution

It introduces a tailored field theory approach to analyze inhomogeneous distributions in self-gravitational systems and calculates the entropy for such configurations.

Findings

Inhomogeneous distributions have higher entropy than homogeneous ones.

Clustering increases the entropy of the system.

Entropy increase suggests a natural tendency for clusters to disperse.

Abstract

The microcanonical partition function for self-gravitational system in three dimensional case has been found. Used approach from the field theory of statistical description of the system was tailored to gravitational interacting particles with regard for an arbitrary spatially inhomogeneous particle distribution. The entropy of self-gravitational system has been found from extreme condition for the effective functional. For inhomogeneous distribution particle (formation few cluster of finite size) the entropy are bigger as the entropy homogeneous distribution of particles. The increasing of entropy of self-gravitational system after formation cluster motive tendency to disperse.