The equilibrium and fluctuations of an ideal gas in a rigid container are studied by every student of statistical mechanics. Here, we examine 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.

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