Phase transition in Modified Newtonian Dynamics (MONDian) self-gravitating systems

TL;DR

This paper investigates the statistical mechanics of binary systems under MOND gravity, revealing a sharp phase transition in microcanonical ensembles and a smoother transition in canonical ensembles, with implications for understanding gravitational clustering.

Contribution

It introduces the first analysis of phase transitions in MONDian self-gravitating systems using statistical mechanics in both microcanonical and canonical ensembles.

Findings

Sharp phase transition in microcanonical systems under MOND

Smoother phase transition in canonical systems with a critical temperature

Distinct behavior compared to Newtonian gravity in gravitational clustering

Abstract

We study the statistical mechanics of binary systems under gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems, in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of physical parameters of the binary system.