Thermal equilibrium of an ideal gas in a free-floating box

TL;DR

This paper investigates the equilibrium and fluctuations of an ideal gas in a freely floating box, modeling how the container's motion fluctuates due to gas interactions, with implications for astrophysical systems like black holes in galaxies.

Contribution

It introduces a novel analysis of a freely floating container with an ideal gas, extending traditional models to include the box's motion and fluctuations.

Findings

Derived the velocity and position fluctuation distributions of the floating box.

Showed the model's relevance to astrophysical phenomena such as black hole-star systems.

Identified potential observability of these fluctuations in galactic centers.

Abstract

The equilibrium and fluctuations of an ideal gas in a rigid container are studied by every student of statistical mechanics. Here we study the less well-known case when the box is floating freely; in particular we determine the fluctuations of the box in velocity and position due to interactions with the gas it contains. This system is a toy model for the fluctuations in velocity and position of a black hole surrounded by stars at the center of a galaxy. These fluctuations may be observable in nearby galaxies.