Thermodynamics of a one-dimensional self-gravitating gas with periodic boundary conditions

TL;DR

This paper investigates the thermodynamics of a one-dimensional gravitational gas with periodic boundaries, revealing a phase transition from uniform to inhomogeneous density states, supported by theoretical analysis and numerical simulations.

Contribution

It introduces a novel model of a 1D gravitational gas with periodic boundary conditions and characterizes its phase transition behavior.

Findings

Existence of a phase transition at a critical temperature

Uniform density above the critical temperature

Inhomogeneous density below the critical temperature

Abstract

We study the thermodynamical properties of a one-dimensional gas with one-dimensional gravitational interactions, and placed in a uniform mass background. Periodic boundary conditions are implemented as a modification of the potential consisting of a sum over mirror images (Ewald sum), regularized with an exponential cut-off. The system has a phase transition at a critical temperature. Above the critical temperature the gas density is uniform, while below the critical point the system becomes inhomogeneous. Numerical simulations of the model confirms the existence of the phase transition, and are in good agreement with the theoretical results.