Inhomogeneous distribution of particles and temperature in self-gravitating system

TL;DR

This paper introduces a new non-equilibrium statistical approach to analyze inhomogeneous particle and temperature distributions in self-gravitating systems, deriving their thermodynamic properties and stability criteria.

Contribution

It proposes a novel method using a non-equilibrium statistical operator and saddle-point approximation to study inhomogeneous distributions in self-gravitating systems, including new stability parameters.

Findings

Derived the equation of state for self-gravitating systems.

Identified a new length scale for statistical instability.

Calculated parameters for spatial inhomogeneity of particles and temperature.

Abstract

Self-gravitating system are non-equilibrium a priory. A new approach is proposed, which employs a non-equilibrium statistical operator into account inhomogeneous distribution of particles and temperature. The method involves the saddle - point procedure to find the dominant contribution to the partition function and thus to obtain all thermodynamic parameters of the system. Probable peculiar features in the behavior of self-gravitating system are considered for various condition. The equation of state for self-gravitating system has been obtained. A new length of statistical instability and parameter of the spatial inhomogeneous distribution of particles and temperature are obtained for real gravitating system.