# Nonequilibrium self-gravitational system

## TL;DR

This paper proposes a novel non-equilibrium statistical approach using a non-equilibrium statistical operator to describe inhomogeneous and temperature-varying self-gravitational systems, addressing divergence issues in traditional models.

## Contribution

It introduces a new method based on non-equilibrium statistical operators to model inhomogeneous self-gravitational systems with spatially varying temperature.

## Key findings

- Describes inhomogeneous particle distribution in gravitational systems.
- Accounts for temperature variation within the system.
- Provides a saddle point method for spatial inhomogeneity.

## Abstract

The density of states of self-gravitational system diverges when the particles are spread to infinity. Other problem based an inhomogeneous distribution of particles,which motivate the gravitational interaction. In this sense the statistical mechanics of self-gravitational system is essentially an non-equilibrium problem. A new possible approach to statistical description of self-gravitational system has been proposed. The approach based on non-equilibrium statistical operator, which allow take into account inhomogeneous distribution particle and temperature in self gravitational system. The saddle point procedure, which used in the given method describes the spatially inhomogeneous distribution in self gravitational system accompanied by temperature changing.